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  • 1
    Electronic Resource
    Electronic Resource
    Progressive global random search of continuous functions (1978)
    Springer
    Mathematical programming 15 (1978), S. 330-342 
    Details
    ISSN: 1436-4646
    Keywords: Global Optimization ; Random Search ; Convergence ; Sequential Minimization ; Lipschitz Functions ; Stochastic Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A sequential random search method for the global minimization of a continuous function is proposed. The algorithm gradually concentrates the random search effort on areas neighboring the global minima. A modification is included for the case that the function cannot be exactly evaluated. The global convergence and the asymptotical optimality of the sequential sampling procedure are proved for both the stochastic and deterministic optimization problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01609037
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  • 2
    Electronic Resource
    Electronic Resource
    Tenth International Symposium on Mathematical Programming (1978)
    Springer
    Mathematical programming 15 (1978), S. 364-364 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01609044
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  • 3
    Electronic Resource
    Electronic Resource
    Least distance methods for the scheme of polytopes (1978)
    Springer
    Mathematical programming 15 (1978), S. 1-11 
    Details
    ISSN: 1436-4646
    Keywords: APL-Codes ; Polytope ; Point Set ; Vertices ; Faces ; Facets ; Quadratic Programming ; Distance ; Decomposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Methods are described and APL-codes are supplied to find vertices, edges, other faces and facets of polytopes given by point sets. The basic subroutine is a simplicial decomposition version of least distance, i.e. quadratic, programming. Computational experience indicates high efficiency.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01608995
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  • 4
    Electronic Resource
    Electronic Resource
    Editorial policy (1978)
    Springer
    Mathematical programming 14 (1978), S. 127-127 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588960
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  • 5
    Electronic Resource
    Electronic Resource
    Algorithms for nonlinear constraints that use lagrangian functions (1978)
    Springer
    Mathematical programming 14 (1978), S. 224-248 
    Details
    ISSN: 1436-4646
    Keywords: Augmented Lagrangian ; Lagrangian Function ; Nonlinear Constraints ; Nonlinear Programming ; Optimization Algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Lagrangian functions are the basis of many of the more successful methods for nonlinear constraints in optimization calculations. Sometimes they are used in conjunction with linear approximations to the constraints and sometimes penalty terms are included to allow the use of algorithms for unconstrained optimization. Much has been discovered about these techniques during the last eight years and this paper gives a view of the progress and understanding that has been achieved and its relevance to practical algorithms. A particular method is recommended that seems to be more powerful than the author believed to be possible at the beginning of 1976.
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    URL: http://dx.doi.org/10.1007/BF01588967
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  • 6
    Electronic Resource
    Electronic Resource
    The Mathematical Programming Society (1978)
    Springer
    Mathematical programming 14 (1978), S. 262-262 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588969
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  • 7
    Electronic Resource
    Electronic Resource
    The reformulation of two mixed integer programming problems (1978)
    Springer
    Mathematical programming 14 (1978), S. 325-331 
    Details
    ISSN: 1436-4646
    Keywords: Integer Programming ; Formulation ; Models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Two practical problems are described, each of which can be formulated in more than one way as a mixed integer programming problem. The computational experience with two formulations of each problem is given. It is pointed out how in each case a reformulation results in the associated linear programming problem being more constrained. As a result the reformulated mixed integer problem is easier to solve. The problems are a multi-period blending problem and a mining investment problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588974
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  • 8
    Electronic Resource
    Electronic Resource
    Numerically stable methods for quadratic programming (1978)
    Springer
    Mathematical programming 14 (1978), S. 349-372 
    Details
    ISSN: 1436-4646
    Keywords: Indefinite Quadratic Programming ; Matrix Factorizations ; Numerical Software
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Numerically stable algorithms for quadratic programming are discussed. A new algorithm is described for indefinite quadratic programming which utilizes methods for updating positivedefinite factorizations only. Consequently all the updating procedures required are common to algorithms for linearly-constrained optimization. The new algorithm can be used for the positive-definite case without loss of efficiency.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588976
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  • 9
    Electronic Resource
    Electronic Resource
    A mathematical programming system for preference and compatibility maximized menu planning and scheduling (1978)
    Springer
    Mathematical programming 15 (1978), S. 63-76 
    Details
    ISSN: 1436-4646
    Keywords: Menu Planning ; Separation Scheduling ; Menu Scheduling ; Decomposition ; Non-linear Programming ; Binary Knapsack Problem ; Lagrangian Relaxation ; Transportation Problem ; Branch and Bound
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper, the analytical representation of food preference is used in a separable non-linear program to yield the serving frequencies of menu items for a finite time horizon. The frequencies obtained in this way insure cost and nutritional control. Subsequently, the scheduling problem dealing with item assignments to meals and days is formulated as an integer program consisting of several transportation problems linked by weekly nutritional constraints. This problem is solved using a branch and bound algorithm which employs Lagrangian relaxation to obtain bounds and to decide on branching strategy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01609000
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  • 10
    Electronic Resource
    Electronic Resource
    On equivalent representations of certain multicommodity networks as single commodity flow problems (1978)
    Springer
    Mathematical programming 15 (1978), S. 92-99 
    Details
    ISSN: 1436-4646
    Keywords: Network Flows ; Multicommodity Networks
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Several classes of multicommodity networks have been shown to have the property that they can be transformed to equivalent uncapacitated single commodity flow problems. We show that many of these networks can be further reduced to smaller, semi-capacitated flow problems using the inverse of a result of Ford and Fulkerson. This appears to be a useful computationally-oriented tool for developing practically efficient algorithms. These concepts are also used to establish a generalization of a previous result concerning multicommodity transportation problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01609003
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  • 11
    Electronic Resource
    Electronic Resource
    Formation of the international association for statistical computing (1978)
    Springer
    Mathematical programming 15 (1978), S. 119-120 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01609008
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  • 12
    Electronic Resource
    Electronic Resource
    A parametric linear complementarity problem involving derivatives (1978)
    Springer
    Mathematical programming 15 (1978), S. 146-154 
    Details
    ISSN: 1436-4646
    Keywords: Linear Complementarity Problem ; Principal Pivoting Algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The problem considered in this paper is given by the conditions:w = q + tp + Mz, w ≥ 0,ż ≥ 0,w T ż = 0, where a dot denotes the derivative with respect to the scalar parametert ≥ 0. In this problem,q, p aren-vectors withq ≥ 0 andM is an byn P-matrix. This problem arises in a certain basic problem in the field of structural mechanics. The main result in this paper is the existence and uniqueness theorem of a solution to this problem. The existence proof is constructive providing a computational method of obtaining the solution asymptotically.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01609013
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  • 13
    Electronic Resource
    Electronic Resource
    A subgradient algorithm for certain minimax and minisum problems (1978)
    Springer
    Mathematical programming 15 (1978), S. 130-145 
    Details
    ISSN: 1436-4646
    Keywords: Minimax Problems ; Minisum Problems ; Nondifferentiable Optimization ; Subgradients ; Location Problems ; Linear Approximation Problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present a subgradient algorithm for minimizing the maximum of a finite collection of functions. It is assumed that each function is the sum of a finite collection of basic convex functions and that the number of different subgradient sets associated with nondifferentiable points of each basic function is finite on any bounded set. Problems belonging to this class include the linear approximation problem and both the minimax and minisum problems of location theory. Convergence of the algorithm to an epsilon-optimal solution is proven and its effectiveness is demonstrated by solving a number of location problems and linear approximation problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01609012
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  • 14
    Electronic Resource
    Electronic Resource
    An asynchronous parallel newton method (1988)
    Springer
    Mathematical programming 42 (1988), S. 363-374 
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    ISSN: 1436-4646
    Keywords: Newton method ; parallel algorithms ; superlinear convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A parallel Newton method is described for the minimization of a twice continuously differentiable uniformly convex functionF(x). The algorithm generates a sequence {x j } which converges superlinearly to the global minimizer ofF(x).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589411
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  • 15
    Electronic Resource
    Electronic Resource
    Generalized polymatroids and submodular flows (1988)
    Springer
    Mathematical programming 42 (1988), S. 489-563 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Polyhedra related to matroids and sub- or supermodular functions play a central role in combinatorial optimization. The purpose of this paper is to present a unified treatment of the subject. The structure of generalized polymatroids and submodular flow systems is discussed in detail along with their close interrelation. In addition to providing several applications, we summarize many known results within this general framework.
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    URL: http://dx.doi.org/10.1007/BF01589418
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  • 16
    Electronic Resource
    Electronic Resource
    S3 sets. An extension of the Beale-Tomlin special ordered sets (1988)
    Springer
    Mathematical programming 42 (1988), S. 113-123 
    Details
    ISSN: 1436-4646
    Keywords: Scheduling ; large-scale 0–1 model ; variable fixing ; coefficient reduction ; special ordered sets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this work an extension of the Beale-Tomlin special ordered sets is introduced that has proved to be efficient for solving certain types of open shop scheduling problems. Besides their usual characteristics, exclusivity constraints in the jobs are allowed, more general than tree-like precedence structures are considered, and semi-active schedules that cannot be labeled as non-optimal solutions may occur. The problem is formulated as a large-scale 0–1 model. Computational experience on some real-life problems is reported.
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    URL: http://dx.doi.org/10.1007/BF01589396
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  • 17
    Electronic Resource
    Electronic Resource
    Impacs - A bus crew scheduling system using integer programming (1988)
    Springer
    Mathematical programming 42 (1988), S. 181-187 
    Details
    ISSN: 1436-4646
    Keywords: Branch and bound ; bus crew scheduling ; integer programming ; scheduling ; set covering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    URL: http://dx.doi.org/10.1007/BF01589402
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  • 18
    Electronic Resource
    Electronic Resource
    Dual coordinate step methods for linear network flow problems (1988)
    Springer
    Mathematical programming 42 (1988), S. 203-243 
    Details
    ISSN: 1436-4646
    Keywords: Network flows ; relaxation ; distributed algorithms ; complexity ; asynchronous algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We review a class of recently-proposed linear-cost network flow methods which are amenable to distributed implementation. All the methods in the class use the notion ofε-complementary slackness, and most do not explicitly manipulate any “global” objects such as paths, trees, or cuts. Interestingly, these methods have stimulated a large number of newserial computational complexity results. We develop the basic theory of these methods and present two specific methods, theε-relaxation algorithm for the minimum-cost flow problem, and theauction algorithm for the assignment problem. We show how to implement these methods with serial complexities of O(N 3 logNC) and O(NA logNC), respectively. We also discuss practical implementation issues and computational experience to date. Finally, we show how to implementε-relaxation in a completely asynchronous, “chaotic” environment in which some processors compute faster than others, some processors communicate faster than others, and there can be arbitrarily large communication delays.
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    URL: http://dx.doi.org/10.1007/BF01589405
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  • 19
    Electronic Resource
    Electronic Resource
    Parallel application of block-iterative methods in medical imaging and radiation therapy (1988)
    Springer
    Mathematical programming 42 (1988), S. 307-325 
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    ISSN: 1436-4646
    Keywords: Full discretization ; computerized tomography ; image reconstruction ; radiotherapy treatment planning ; block-iterative algorithms ; parallel computations ; Cimmino's algorithm ; entropy maximization ; classification of algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Some row-action algorithms which exploit special objective function and constraints structure have proven advantageous for solving huge and sparse feasibility or optimization problems. Recently developed block-iterative versions of such special-purpose methods enable parallel computation when the underlying problem is appropriately decomposed. This opens the door for parallel computation in image reconstruction problems of computerized tomography and in the inverse problem of radiation therapy treatment planning, all in their fully discretized modelling approach. Since there is more than one way of deriving block-iterative versions of any row-action method, the choice has to be made with reference to the underlying real-world problem.
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    URL: http://dx.doi.org/10.1007/BF01589408
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  • 20
    Electronic Resource
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    Decomposition of linear programs using parallel computation (1988)
    Springer
    Mathematical programming 42 (1988), S. 391-405 
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    ISSN: 1436-4646
    Keywords: Linear programming ; large-scale-systems ; decomposition ; parallel computing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper describes DECOMPAR: an implementation of the Dantzig-Wolfe decomposition algorithm for block-angular linear programs using parallel processing of the subproblems. The software is based on a robust experimental code for LP decomposition and runs on the CRYSTAL multicomputer at the University of Wisconsin-Madison. Initial computational experience is reported. Promising directions in future development of this approach are discussed.
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    URL: http://dx.doi.org/10.1007/BF01589413
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  • 21
    Electronic Resource
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    A matroid algorithm and its application to the efficient solution of two optimization problems on graphs (1988)
    Springer
    Mathematical programming 42 (1988), S. 471-487 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We address the problem of finding a minimum weight baseB of a matroid when, in addition, each element of the matroid is colored with one ofm colors and there are upper and lower bound restrictions on the number of elements ofB with colori, fori = 1, 2,⋯,m. This problem is a special case of matroid intersection. We present an algorithm that exploits the special structure, and we apply it to two optimization problems on graphs. When applied to the weighted bipartite matching problem, our algorithm has complexity O(|E∥V|+|V| 2log|V|). HereV denotes the node set of the underlying bipartite graph, andE denotes its edge set. The second application is defined on a general connected graphG = (V,E) whose edges have a weight and a color. One seeks a minimum weight spanning tree with upper and lower bound restrictions on the number of edges with colori in the tree, for eachi. Our algorithm for this problem has complexity O(|E∥V|+m 2 |V|+ m|V| 2). A special case of this constrained spanning tree problem occurs whenV * is a set of pairwise nonadjacent nodes ofG. One must find a minimum weight spanning tree with upper and lower bound restrictions on the degree of each node ofV *. Then the complexity of our algorithm is O(|V∥E|+|V * ∥V| 2). Finally, we discuss a new relaxation of the traveling salesman problem.
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    URL: http://dx.doi.org/10.1007/BF01589417
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  • 22
    Electronic Resource
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    On optimality conditions in nondifferentiable programming (1978)
    Springer
    Mathematical programming 14 (1978), S. 73-86 
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    ISSN: 1436-4646
    Keywords: Gradient ; Subdifferential ; Generalized Gradient ; Optimality Conditions ; Nondifferentiability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper is devoted to necessary optimality conditions in a mathematical programming problem without differentiability or convexity assumptions on the data. The main tool of this study is the concept of generalized gradient of a locally Lipschitz function (and more generally of a lower semi-continuous function). In the first part, we consider local extremization problems in the unconstrained case for objective functions taking values in (−∞, +∞]. In the second part, the constrained case is considered by the way of the cone of adherent displacements. In the presence of inequality constraints, we derive in the third part optimality conditions in the Kuhn—Tucker form under a constraint qualification.
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    URL: http://dx.doi.org/10.1007/BF01588951
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  • 23
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    A quadratic network optimization model for equilibrium single commodity trade flows (1978)
    Springer
    Mathematical programming 14 (1978), S. 98-107 
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    ISSN: 1436-4646
    Keywords: Network Flows ; Equilibrium Trade ; Quadratic Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract When supply and demand curves for a single commodity are approximately linear in each ofN regions and interregional transportation costs are linear, then equilibrium trade flows can be computed by solving a quadratic program of special structure. An equilibrium trade flow exists in which the routes carrying positive flow form a forest, and this solution can be efficiently computed by a tree growing algorithm.
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    URL: http://dx.doi.org/10.1007/BF01588953
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  • 24
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    Referees 1977 (1978)
    Springer
    Mathematical programming 14 (1978), S. 125-125 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    URL: http://dx.doi.org/10.1007/BF01588958
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  • 25
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    The Mathematical Programming Society (1978)
    Springer
    Mathematical programming 14 (1978), S. 126-126 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    URL: http://dx.doi.org/10.1007/BF01588959
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  • 26
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    Second order characterizations of pseudoconvex functions (1978)
    Springer
    Mathematical programming 14 (1978), S. 170-185 
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    ISSN: 1436-4646
    Keywords: Nonlinear Programming ; Pseudoconvexity ; Second order Characterizations ; Extended Hessians ; Bordered Determinants ; Quadratic Functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Second order characterizations for (strictly) pseudoconvex functions are derived in terms of extended Hessians and bordered determinants. Additional results are presented for quadratic functions.
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    Editorial policy (1978)
    Springer
    Mathematical programming 14 (1978), S. 263-263 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    URL: http://dx.doi.org/10.1007/BF01588970
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  • 28
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    Symposium on constructive approaches to Mathematical Models (1978)
    Springer
    Mathematical programming 14 (1978), S. 378-378 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    URL: http://dx.doi.org/10.1007/BF01588978
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  • 29
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    International Symposium on systems optimization and analysis (1978)
    Springer
    Mathematical programming 14 (1978), S. 380-380 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    URL: http://dx.doi.org/10.1007/BF01588980
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  • 30
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    The Mathematical Programming Society (1978)
    Springer
    Mathematical programming 14 (1978), S. 381-381 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    URL: http://dx.doi.org/10.1007/BF01588981
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  • 31
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    Convex optimization and lagrange multipliers (1978)
    Springer
    Mathematical programming 15 (1978), S. 87-91 
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    ISSN: 1436-4646
    Keywords: Lagrange Multipliers ; Constrained Convex Optimization ; Kuhn—Tucker Theorem ; Duality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The duality theorem of linear programming is used to prove several results on convex optimization. This is done without using separating hyerplane theorems.
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    URL: http://dx.doi.org/10.1007/BF01609002
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  • 32
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    A note on a theorem of Yamamuro (1978)
    Springer
    Mathematical programming 15 (1978), S. 110-113 
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    ISSN: 1436-4646
    Keywords: Fixed Point Computation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Conditions are presented which are necessary for the existence of a regular fixed point of aC 1 map.
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    URL: http://dx.doi.org/10.1007/BF01609006
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  • 33
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    Editorial policy (1978)
    Springer
    Mathematical programming 15 (1978), S. 122-122 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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    URL: http://dx.doi.org/10.1007/BF01609010
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  • 34
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    A generalized knapsack problem with variable coefficients (1978)
    Springer
    Mathematical programming 15 (1978), S. 162-176 
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    ISSN: 1436-4646
    Keywords: Mixed Integer Programming ; Knapsack Problem ; Branch and Bound Method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The ordinary knapsack problem is to find the optimal combination of items to be packed in a knapsack under a single constraint on the total allowable resources, where all coefficients in the objective function and in the constraint are constant. In this paper, a generalized knapsack problem with coefficients depending on variable parameters is proposed and discussed. Developing an effective branch and bound algorithm for this problem, the concept of relaxation and the efficiency function introduced here will play important roles. Furthermore, a relation between the algorithm and the dynamic programming approach is discussed, and subsequently it will be shown that the ordinary 0–1 knapsack problem, the linear programming knapsack problem and the single constrained linear programming problem with upper-bounded variables are special cases of the interested problem. Finally, practical applications of the problem and its computational experiences will be shown.
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    A continuous variable representation of the traveling salesman problem (1978)
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    Mathematical programming 15 (1978), S. 211-213 
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    Keywords: Traveling Salesman Problem ; Cardinality Constraints ; Hamiltonian Circuits ; Network Flow Problems
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    Topics: Computer Science , Mathematics
    Notes: Abstract The classic traveling salesman problem is characterized in terms of continuous flows on a specially constructed non-conservative network, in 2n − 1 linear constraints and a cardinality constraint. It is shown that every solution to the network problem is a hamiltonian circuit.
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    A note on ‘monotone optimal policies for markov decision processes’ (1978)
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    Mathematical programming 15 (1978), S. 220-222 
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    ISSN: 1436-4646
    Keywords: Dynamic Decision Model ; Monotone Optimal Decision Functions
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    Topics: Computer Science , Mathematics
    Notes: Abstract The purpose of this short note is to correct some oversights in [1]. More precisely, we point out that stronger assumptions have to be imposed on the decision model (in order to use results in [2]) and present a counterexample to a comment to [1, Theorem 3.1].
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    A note on ‘new algorithms for constrained minimax optimization’ (1978)
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    Mathematical programming 15 (1978), S. 239-242 
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    ISSN: 1436-4646
    Keywords: Minimax Optimization ; Nonlinear Programming
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    Notes: Abstract An unconstrained minimax algorithm of Charalambous and Conn is easily modified to solve the constrained case. Here we present some numerical results and find that this algorithm compares favourably to those of Dutta and Vidyasagar.
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    Optimal conditioning in the convex class of rank two updates (1978)
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    Mathematical programming 15 (1978), S. 247-260 
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    ISSN: 1436-4646
    Keywords: Quasi-Newton Method ; Optimal Conditioning ; Rank-two Update
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    Notes: Abstract Davidon's new quasi-Newton optimization algorithm selects the new inverse Hessian approximation $$\bar H$$ at each step to be the “optimally conditioned” member of a certain one-parameter class of rank two updates to the last inverse Hessian approximationH. In this paper we show that virtually the same goals of conditioning can be achieved while restricting $$\bar H$$ to the convex class of updates, which are bounded by the popular DFP and BFGS updates. This suggests the computational testing of alternatives to the “optimal conditioning” strategy.
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    An implementation of some implicit function theorems with applications to sensitivity analysis (1978)
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    Mathematical programming 15 (1978), S. 261-267 
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    ISSN: 1436-4646
    Keywords: Sensitivity Analysis in Nonlinear Programming ; Computational Aspects ; Chemical Equilibrium Problems ; Entropy Maximization Problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper presents an implementation of some recent results of Bigelow and Shapiro [1]. These implicit function theorems are shown to provide a convenient means of performing certain types of sensitivity analysis, in particular updating the lagrange multipliers, associated with particular classes of problems. As a result we extend the usual sensitivity analysis results to include improving estimates of the effect of changing the right-hand sides of constraints. Examples of chemical equilibrium and entropy maximization models are used to illustrate the results.
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    A lower bound for the controlling parameters of the exact penalty functions (1978)
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    Mathematical programming 15 (1978), S. 278-290 
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    Keywords: Constrained Optimization ; Exact Penalty Functions ; Nondifferentiable Functions
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    Topics: Computer Science , Mathematics
    Notes: Abstract The purpose of this paper is to present new exact penalty functions and discuss their properties. A lower bound on the controlling parameters is given, for which above this value, the optimum of the exact penalty function coincides with the optimum of the nonlinear programming problem.
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    Testing of a large-scale network optimization program (1978)
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    Mathematical programming 15 (1978), S. 291-314 
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    ISSN: 1436-4646
    Keywords: Network Flow Problems ; Computational Results—Efficiency—Comparison ; Specific problems in mathematical programming ; Computational Experiments ; Pivotal Selection Methods ; Starting Strategies ; Scaling Procedure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper describes the experimental results of testing a “large-scale” program for solving minimum-cost network flow problems. With this program, general structure transshipment problems with over ten thousand nodes and thirty thousand arcs have been easily solved without resorting to auxiliary storage. The algorithm is a variant of the primal revised simplex method; the computer code is called LPNET illustrating the close connection between linear programming and network graphs. This approach substantially improves computer processing timeand core storage, especially for relatively large network problems. The results of these experiments are provided. It is emphasized that an organized experimental design and a detailed series of empirical tests are crucial for an efficient implementation.
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    The decomposition of nonlinear problems (1978)
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    Mathematical programming 15 (1978), S. 360-362 
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    Keywords: Nonlinear Decomposition ; Nonlinear Programming
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    Notes: Abstract We show that under certain conditions nonlinear programming problems can be decomposed into a series of smaller problems. A Decomposition Theorem and example are presented.
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    Nominations for 1979 elections (1978)
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    Mathematical programming 15 (1978), S. 363-363 
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    Mathematical programming study 9 Mathematical Programming in use (1978)
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    Mathematical programming 15 (1978), S. 365-368 
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    Optimal design of a manpower system (1978)
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    Mathematical programming 15 (1978), S. 26-35 
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    Keywords: Manpower Planning ; Column Generation ; Network Flows ; Shortest Path ; System Design
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    Topics: Computer Science , Mathematics
    Notes: Abstract An equilibrium model of a manpower system is developed based on the notion of a career flow. Institutional constraints and measures of system performance are linear functions of the career flow. A typical optimal design problem is formulated and a solution procedure is developed. The optimization problem is a generalized linear program in which columns are generated by solving a shortest path problem. Upper and lower bounds on the optimal value function can be developed at each stage of the calculations.
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    Piecewise convex programs (1978)
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    Mathematical programming 15 (1978), S. 53-62 
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    ISSN: 1436-4646
    Keywords: Convex Program ; Decomposition ; Cutting Plane Algorithm ; Stochastic Quadratic Program with Recourse
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    Notes: Abstract A piecewise convex program is a convex program such that the constraint set can be decomposed in a finite number of closed convex sets, called the cells of the decomposition, and such that on each of these cells the objective function can be described by a continuously differentiable convex function. In a first part, a cutting hyperplane method is proposed, which successively considers the various cells of the decomposition, checks whether the cell contains an optimal solution to the problem, and, if not, imposes a convexity cut which rejects the whole cell from the feasibility region. This elimination, which is basically a dual decomposition method but with an efficient use of the specific structure of the problem is shown to be finitely convergent. The second part of this paper is devoted to the study of some special cases of piecewise convex program and in particular the piecewise quadratic program having a polyhedral constraint set. Such a program arises naturally in stochastic quadratic programming with recourse, which is the subject of the last section.
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    Ein Verfahren zur iterativen Einschließung des positiven Eigenvektors einer irreduziblen, nichtnegativen Matrix (1978)
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    Computing 20 (1978), S. 27-34 
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    Topics: Computer Science
    Description / Table of Contents: Abstract We develop a new iteration scheme giving bounds for the positive eigenvector of a nonnegative and irreducible matrix and the corresponding eigenvalue and test it on some examples.
    Notes: Zusammenfassung Wir geben ein neues Iterationsverfahren an, das Schranken für den positiven Eigenvektor einer nichtnegativen, irreduziblen Matrix und des zugehörigen Eigenwerts liefert.
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    Über eine Wahl des Parameters beim Parallelenverfahren (Parallel-Chord-Method) (1978)
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    Computing 20 (1978), S. 17-26 
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    Description / Table of Contents: Abstract Due to the free parameter in the fixed-point equation of the parallel-chord-method, it is possible to reduce the Lipschitz constant of the contraction mapping. By use of this reduction, it is possible in suitable cases to generate the contraction property of the mapping. If the mapping possesses this property, then this is also true for the mapping with the parameter determined here. In addition, both an improved error estimate for the sequences of iterates and a smaller convergence factor are obtained. An example is presented.
    Notes: Zusammenfassung Mit Hilfe des freien Parameters in der Fixpunktgleichung des Parallelenverfahrens ist es möglich, die Lipschitz-Konstante der kontrahierenden Abbildung zu verkleinern. Durch diese Verkleinerung kann in geeigneten Fällen eine kontrahierende Abbildung erzeugt werden. Ist die Abbildung bereits kontrahierend, ist sie auch kontrahierend für den berechneten Wert des Parameters. Ferner ergibt sich neben einer verbesserten Fehlerabschätzung für die Iterationsfolgen auch ein kleinerer Konvergenzfaktor. Das Verfahren wird an Hand eines Beispiels erläutert.
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    Zur Approximation von Schalen mit hybriden Elementen (1978)
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    Computing 20 (1978), S. 75-94 
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    Description / Table of Contents: Abstract A theory of hybrid finite element approximation is developed for a class of shell problems. Though it is applied only to the special case of clamped shallow shells with regular triangularization the results may be of larger interest comparing the predicted convergence rate with the numerical outcome of some applications of the hybrid finite element method. The convergence speed can only be increased by higher degrees of the approximation and the stresses at the edges correspondingly. The use of a so-called rank condition plays a fundamental role in the study. Weak coerciveness of the under lyigg bilinear form for the derivation of hybrid elements is proved by showing the existence of a stationary point.
    Notes: Zusammenfassung Dieser Beitrag liefert eine Theorie der Finite-Element-Approximation für eine Klasse von Schalenproblemen. Obgleich diese nur für den Fall der eingespannten flachen Schale mit regulärer Triangulierung ausführlich dargestellt wird, sind die Ergebnisse darüberhinaus von Interesse, da die abgeleiteten Konvergenzordnungen das Verhalten numerischer Näherungslösungen aus anderen Anwendungen der hybriden Finite-Element-Methode erklären helfen. Die Konvergenzgeschwindigkeit kann nur verbessert werden durch gleichzeitige Erhöhung der Ansatzgrade für die Verschiebungen im Elementinnern und für die Spannungen auf den Rändern. Die Einhaltung einer sogenannten Rangbedingung hat zentrale Bedeutung. Die schwache Koerzitivität der für die Ableitung hybrider Elemente verwendeten Bilinearform ist durch den Nachweis der Existenz eines stationären Werts gesichert.
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    Interval forms of Newtons method (1978)
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    Computing 20 (1978), S. 153-163 
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    Description / Table of Contents: Zusammenfassung Eine verbesserte Darstellung Newtonscher Intervall-Verfahren wird diskutiert. Es wird dabei gezeigt, daß man bestimmte Intervalle in den Verfahren durch reelle Zahlen ersetzen kann. Dadurch werden die Konvergenzeigenschaften der Verfahren verbessert.
    Notes: Abstract Improved forms of some interval Newton Methods are given. It is shown that certain intervals in the methods can be replaced by real numbers. This improves the convergence properties of the methods.
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    Eine rundungsgenaue Formel zur maschinellen Berechnung der Prager-Oettli-Schranke (1978)
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    Computing 20 (1978), S. 177-182 
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    Description / Table of Contents: Abstract The bound of Prager-Oettli for the input error of a linear system of equations is computed via a new formula which guarantees strictness of the bound in spite of roundoff errors.
    Notes: Zusammenfassung Die Schranke von Prager-Oettli für den Eingangsfehler eines linearen Gleichungssystems wird über eine neue Formel berechnet, die trotz der Rundungsfehler die Schärfe der Schranke sichert.
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    Iterated defect correction for differential equations part I: theoretical results (1978)
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    Computing 20 (1978), S. 207-228 
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    ISSN: 1436-5057
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die Iterierte Defektkorrektur (IDeC) ist ein Verfahren zur schrittweisen Verbesserung einer Näherungslösung eines gegebenen ProblemsFy=0. Eines der wichtigsten Anwendungsgebiete dieses Prinzips sind Differentialgleichungen. Die IDeC kann dort als Methode zur Verbesserung der Ordnung eines Diskretisierungsverfahrens, und damit zur Verbesserung der Genauigkeit eingesetzt werden. In der vorliegenden Arbeit wird ein Metaalgorithmus für die Klasse, der IDeC-Verfahren für Differential-gleichungen vorgestellt und analysiert. Für jeden “Baustein” dieses Metaalgorithmus werden Bedingungen angegeben, die es gewährleisten, daß eine bestimmte Ordnung erreicht wird. Diese Bedingungen sind von großer praktischer Bedeutung, wenn IDeC-Verfahren als Computer-Programme implementiert werden sollen.
    Notes: Abstract Iterated Defect Correction (IDeC) is a technique for improving successively an approximate solution of a given problemFy=0. One of the most important fields of application of this principle are differential equations. Here, IDeC can be used as a technique for increasing the order of a discretization method and thus for improving the accuracy. In this paper a metalgorithm for the class of IDeC-methods for differential equations is presented and analyzed. For every component of this metalgorithm conditions are given which guarantee a certain order of accuracy. These conditions are of particular importance for practical applications, as far as the implementation of IDeC-methods is concerned.
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    Ein Abbrechkriterium für einen numerischen Algorithmus (1978)
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    Computing 20 (1978), S. 257-265 
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    Topics: Computer Science
    Description / Table of Contents: Abstract A termination criterion by Nickel (Theorem 6, [1]) for guaranteeing the numerical convergence for locally stable and consistent algorithms is generalized. The assumption |x ν+2,x ν+1|≤L|x ν+1,x ν| (0≤L〈1,L real constant) of the approximation sequence {x ν} to the solution is replaced by the convergence of the progression $$\sum\limits_{v = 1}^\infty {|x,x_{v + 1} |/Q^v (0〈 Q〈 1)} $$ . Therefore the theorem of this paper is applicable to a large number of numerical procedures, for which untill now no termination criterion has been known (for example: Rombergprocedure). In particular this weakening is important for the computation of approximation solutions for integral equations.
    Notes: Zusammenfassung Ein Abbrechkriterium von Nickel (Satz 6, [1]) zur Sicherung der numerischen Konvergenz bei lokal stabilen und konsistenten Algorithmen wird verallgemeinert. Statt der Eigenschaft |x ν+2,x ν+1|≤L|x ν+1,x ν| (0≤L〈1,L von ν ∈ ℕ unabhängig) der Näherungsfolge {x ν} zur Lösungx reicht die Konvergenz der Reihe $$\sum\limits_{v = 1}^\infty {|x,x_{v + 1} |/Q^v (0〈 Q〈 1)} $$ aus. Damit ist der Satz dieser Arbeit bei einer großen Klasse von numerischen Verfahren anwendbar, für die bisher noch kein Abbrechkriterium bekannt ist (z. B. dem Romberg-Verfahren). Insbesondere ist diese Abschwächung zur Berechnung von Näherungslösungen bei Integralgleichungen wichtig.
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    The nonlinear Volterra equation of Abel's kind and its numerical treatment (1978)
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    Computing 20 (1978), S. 307-324 
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Ausgehend von einem Existenz- und Eindeutigkeitssatz für die Lösung einer verallgemeinerten Volterra-Integralgleichung zweiter Art wird die Existenz und Eindeutigkeit der Lösung der hier behandelten nichtlinearen, schwach singulären Volterra-Integralgleichung erster Art untersucht. Es wird ein numerisches Verfahren der Ordnung 2 bzw. 3 angegeben. Der Konvergenzbeweis basiert in beiden Fällen auf einem Lemma über die Beschränktheit einer speziellen Differenzenungleichung. An zwei numerischen Beispielen werden die theoretischen Ergebnisse demonstriert.
    Notes: Abstract Starting from an existence and uniqueness theorem for a generalized nonsingular second kind Volterra equation existence and uniqueness for the solution of the nonlinear, weakly singular first kind Volterra equation is examined. A new type of numerical method is developed. A basic lemma concerning the boundedness of a special difference inequality is given and order two or three convergence of the method is shown. Two numerical examples illustrate the theoretical results.
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    Über A (α)-stabile Verfahren hoher Konsistenzordnung (1978)
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    Computing 20 (1978), S. 343-350 
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    Topics: Computer Science
    Description / Table of Contents: Abstract For each α ε (0, π/2), the existence ofA (α)-stable linear multistep methods with arbitrary order of consistency is shown by an explicit construction. Some characteristic data of the methods and numerical results are given.
    Notes: Zusammenfassung Es wird in einer expliziten Konstruktion gezeigt, daß für jedes α ε (0, π/2)A (α)-stabile lineare Mehrschrittverfahren beliebiger Konsistenzordnung existieren. Einige charakteristische Daten der Verfahren und numerische Rechnungen werden angegeben.
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    A performance model for preplanned disk sorting (1978)
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    Computing 21 (1978), S. 17-35 
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    ISSN: 1436-5057
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Der Ansatz, Strings, die zusammengemischt werden, auf Magnetplatten vorzuplanen, wird unter Leistungsgesichtspunkten untersucht. Konzepte für die interne Pufferzuordnung, für die Erzeugung der anfänglichen Strings durch ein internes Sortierverfahren, und für die Stringverteilung auf Magnetplatten werden ausgewertet. Ein Algorithmus beschreibt die Konstruktion von suboptimalen Mischbäumen, die planbare Mischbäume genannt werden. Ein Kostenmodell, das auf detaillierte Annahmen der Zuordnung vonk Eingabeplatten und der Planung einesr-Wege-Mischens beruht, wird für das exakte Vorplanen aufgestellt. Zeitbetrachtungen für Sortieren und Mischen, die Hardware-Eigenschaften von Magnetplatten einschließen, zeigen signifikante Zeitgewinne verglichen mit weitverbreiteten Sortier- und Mischverfahren.
    Notes: Abstract The idea of preplanning strings on disks which are merged together is investigated from a performance point of view. Schemes of internal buffer allocation, initial string creation by an internal sort, and string distribution on disks are evaluated. An algorithm is given for the construction of suboptimal merge trees called plannable merge trees. A cost model is presented for accurate preplanning which consists of detailed assumptions on disk allocation fork input disks andr-way merge planning. Timing considerations for sort and merge including hardware characteristics of moveable head disks show a significant gain of time compared to widely used sort/merge applications.
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    Convergence acceleration on a general class of power series (1978)
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    Computing 21 (1978), S. 53-69 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In dieser Arbeit werden mehrere effiziente Methoden zur Berechnung von Funktionen, die durch Potenzenreihen definiert sind, präsentiert. Einfache Computerprogramme für zwei schnelle Algorithmen werden in einem eigenen Beitrag ([9]) angegeben. Die Konvergenzgeschwindigkeiten der vorgeschlagenen Verfahren werden theoretisch untersucht und die erhaltenen Ergebnisse werden an numerischen Beispielen erläutert.
    Notes: Abstract In this paper we present several efficient methods for evaluating functions defined by power series expansions. Simple computer codes for two rapid algorithms are given in a companion paper. The convergence rates of the proposed computational schemes are investigated theoretically and the results are illustrated by numerical examples.
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    On the determination of the weights in multi-dimensional numerical quadrature (1978)
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    Computing 21 (1978), S. 71-79 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Mit Hilfe der Pseudoinversen eines beschränkten linearen Operators von ℝ n inl 2 wird eine Methode zur Konstruktion von Quadraturformeln für die Integration über einem beliebigen beschränktenm-dimensionalen GebietB⊂ℝ m hergeleitet, mit der Eigenschaft, daß der mittlere Fehler in einer vorgeschriebenen FamilieF sowie die Varianz der Rundungsfehler gemäß Sard [8] minimal werden. Sodann wählen wirF als gewichtete Monome und behandeln als Beispiel Integration auf der Oberfläche derm-Kugel.
    Notes: Abstract Using the concept of the generalized inverse of a bounded linear transformation between ℝ n andl 2, a method is given for constructing quadrature rules for integration over an arbitrary boundedm-dimensional regionB⊂ℝ m with the property that the average error over the prescribed familyF of the functions continuous inB as well as the variance of the rounding errors according to Sard [8] are minimal. Then we specializeF to the weighted monomials and treat as an example integration on the surface of them-sphere.
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    Algorithm 38 two computer codes for convergence acceleration (1978)
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    Computing 21 (1978), S. 87-91 
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    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In dieser Arbeit werden zwei Computerprogramme für die Berechnung der Summe einer Potenzenreihe, die einer allgemeinen Klasse zugehört, beschrieben. Die Verwendung der Programme ist mit einem Beispiel erläutert.
    Notes: Abstract This paper describes two computer codes for calculating the sum of power series, belonging to a certain general class. The use of the codes for an illustrative test example is explained.
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    Runge-Kutta integration algorithms with built-in estimates of the accumulated truncation error (1978)
    Springer
    Computing 20 (1978), S. 1-16 
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    ISSN: 1436-5057
    Keywords: Integration ; Runge-Kutta integration ; truncation error ; error estimates ; accumulated error ; accumulated error estimates ; accumulated truncation error ; true error
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird eine Methode für die Entwicklung von Runge-Kutta-Integrationsalgorithmen angegeben, die die Schätzung des globalen Verfahrensfehlers ermöglichen. Mehrere neue Algorithmen 2., 3. und 4. Ordnung werden angeführt. Die Rechenarbeit pro Schritt ist identisch für die neuen Algorithmen und für Algorithmen, die nur eine Schätzung des lokalen Verfahrensfehlers ermöglichen. Numerische Versuche mit den neuen Algorithmen ergeben, daß der geschätzte Fehler den wahren akkumulierten Fehler gut wiedergibt. Außerdem ist der Fehler von derselben Ordnung wie bei gewöhnlichen Runge-Kutta-Algorithmen.
    Notes: Abstract A method is presented for developing Runge-Kutta integration algorithms with built-in estimates of the accumulated truncation error. Several new 2-nd, 3-rd, and 4-th order algorithms are given. The computation per step of the new algorithms is identical to that of algorithms which provide only an estimate of the local truncation error. Numerical experimentation with the new algorithms shows that the estimated error compares very well with the true accumulated error. Further, the error is of the same order as that incurred using traditional Runge-Kutta algorithms.
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    On a method of characteristics for solving a hyperbolic equation of second order (1978)
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    Computing 20 (1978), S. 47-60 
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    Source: Springer Online Journal Archives 1860-2000
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    Description / Table of Contents: Zusammenfassung Das Anfangsrandwertproblem für die hyperbolische Differentialgleichunga(t,x,u)u tt +2b(t,x,u)u tx +c(t,x,u)u xx =d(t,x,u,u t ,u x ) zweiter Ordnung wird mit Hilfe eines Charakteristikenverfahrens gelöst, das keine Differenzengleichungen füru t undu x benutzt. Die Lösung des diskretisierten Problems besitzt eine asymptotische Entwicklung nach geraden Potenzen der Schrittweite. Daher können die numerischen Ergebnisse durch Extrapolation verbessert werden.
    Notes: Abstract The hyperbolic initial-boundary value problem for the second order equationa(t,x,u)u tt +2b(t,x,u)u tx +c(t,x,u)u xx =d(t,x,u,u t ,u x ) is solved by a special method of characteristics involving no difference equations foru t andu x . The discrete solution has an asymptotic expansion in even powers of the step size. Therefore, the numerical results can be improved by extrapolation to the limit.
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    Polynomial least square interval approximation (1978)
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    Computing 20 (1978), S. 165-176 
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    Source: Springer Online Journal Archives 1860-2000
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    Description / Table of Contents: Zusammenfassung Das folgende Problem wird behandelt: gegeben sei eine Menge vonm rechteckigen Gebieten in der Ebene, man finde ein Intervall-Polynom vom Gradn〉m durch diese Gebiete. Dies ist eine Verallgemeinerung des diskreten Problems der kleinsten Quadrate. Drei Verallgemeinerungen der gewöhnlichen Methode der kleinsten Quadrate für Polynome werden betrachtet und an numerischen Beispielen verglichen. Eine dieser Methoden wird empfohlen, da sie in allen Testbeispielen bessere Ergebnisse gibt.
    Notes: Abstract The following problem is treated: given a set ofm rectangular regions in the plane, fit an interval polynomial of degreen〉m through the regions. This is a generalization of the discrete polynomial least squares problem. Three generalizations of the standard methods for the discrete polynomial least squares are considered and compared on numerical examples. One of the methods is recommended since it gives superior results in all cases tested.
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    On scheduling multi-processor systems with algebraic objectives (1978)
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    Computing 20 (1978), S. 189-205 
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    Description / Table of Contents: Zusammenfassung Eines der am besten beschriebenen Modelle kombinatorischer Optimierung ist das Scheduling Problem, bei dem eine endliche Anzahl von Tätigkeiten auf einer festen Anzahl von Maschinen so ausgeführt werden muß, daß eine gegebene Zielfunktion minimiert wird. Jede Tätigkeit benötigt charakteristische Daten wie Bearbeitungszeit, Fertigsteillungstermin, Strafkosten und technologische Nachfolgebeziehungen. Ein algebraischer Ansatz für die Zielfunktion führt zu einem allgemeinen Problem, das alle in der Literatur bekannten klassischen Fälle von Summen und Maximum Zielfunktionen einschließt. Durch die Lösung eines algebraischen Transportproblems wird eine untere Schranke für den Zielfunktionswert bestimmt. Um eine Optimallösung zu erhalten, verwenden wir ein Branch and Bound Verfahren. Weiterhin betrachten wir das allgemeine Job Shop Scheduling Problem mit algebraischer Zielfunktion.
    Notes: Abstract One of the well-studied models of combinatorial optimization is the scheduling problem dealing with a finite set of tasks, which have to be executed on a fixed number of machines so that a given objective is minimized. Each task requires a set of characteristic data like operating time, due date, penalty cost and technological requirements. An algebraic approach to the objective leads to a general problem which includes all classical cases of sum and bottleneck objectives known in literature. By solving an algebraic transportation problem a lower bound for the objective value can be determined. To obtain an optimal solution we employ a branch and bound procedure. Furthermore we consider the general job shop scheduling problem with algebraic objective function.
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    Minimierung der Rechenzeit bei der Berechnung von Lösungen nichtlinearer Integralgleichungen (1978)
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    Computing 20 (1978), S. 325-331 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract The result of this paper is the economizing of cpu-time by identical guaranteed precision of the approximate solution. This is possible by an optimal selection ofn j in every iteration stepj, wheren j is the number of subintervals for the numerical integration. The determination ofn 1,n 2, ... is reduced to the solution of a solvable convex optimization job.
    Notes: Zusammenfassung Es wird die Einsparung von Rechenzeit bei gleicher garantierter Genauigkeit der Näherungslösung ermöglicht. Dies wird erreicht durch eine optimale Wahl vonn j bei jedem Iterationsschrittj, wobein j die Zahl der Teilintervalle für die Quadratur ist. Die Bestimmung vonn 1,n 2,... wird auf die Lösung einer lösbaren konvexen Optimierungsaufgabe zurückgeführt.
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    Komplexitätserfordernisse von Modellen zur optimalen Indexselektion für Datenbanken (1978)
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    Computing 20 (1978), S. 279-290 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
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    Description / Table of Contents: Abstract It is one of the basic questions in designing a database system to determine which attributes to invert. The literature presents a variety of models to solve this question. This paper attempts to give a guideline, under which conditions a primitive model considering only retrieve operations, suffices to determine an optimal solution. The relevance of that question lies in the smaller costs of simpler models.
    Notes: Zusammenfassung Eine wesentliche Fragestellung beim Aufbau eines Datenbanksystems ist die Auswahl der Schlüsselattribute. Bei Inverted-File Systemen ist dies äquivalent zur Auswahl der zu invertierenden Attribute. In diesem Aufsatz wird versucht darzustellen, unter welchen Bedingungen Modelle, die lediglich das Retrieve-Verhalten des Benutzers berücksichtigen, zuverlässige Resultate liefern können. Die Relevanz dieser Fragestellung liegt vor allem in den durch das einfachere Modell verminderten Kosten der Datenbeschaffung und Datenanalyse im DB-Designprozeß.
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    On the convergence of multistep methods for the Cauchy problem for ordinary differential equations (1978)
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    Computing 20 (1978), S. 351-361 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
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    Description / Table of Contents: Zusammenfassung Es wird ein allgemeines, quasilineares, nichtstationäresk-Schrittverfahren für die Lösung des Cauchy-Problems für gewöhnliche Differentialgleichungen untersucht. Ein Konvergenzsatz mit ziemlich schwachen Bedingungen wird angegeben. Die Inkrementfunktion muß nicht Lipschitz-stetig sein; es genügt, wenn diese Funktion die Perron-Bedingung aus der Eindeutigkeitstheorie für das Cauchy-Problem mit nichtabnehmender Vergleichfunktion erfüllt. Das Ergebnis ist eine Erweiterung der Theorie von G. Dahlquist und des letzten Resultats von K. Taubert.
    Notes: Abstract The general form of a quasilinear nonstationaryk-step method for solving of the Cauchy problem for ordinary differential equations is discussed. The convergence theorem is stated under rather weak conditions. It is not assumed that the increment function is Lipschitz-continuous but only that it satisfies the Perron type condition appearing in the uniqueness theory for the Cauchy problem with a nondecreasing comparison function. The result established in the paper is an extension of the theory given by G. Dahlquist and the recent result of K. Taubert.
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    Algorithm 36 SNIFF: Efficient self-tuning algorithm for numerical integration (1978)
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    Computing 20 (1978), S. 363-375 
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    Source: Springer Online Journal Archives 1860-2000
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    Description / Table of Contents: Zusammenfassung Hier wird ein neuer selbsteichender Algorithmus für die Integration der analytischen Funktionen dargestellt. Der Algorithmus wirkt auf das Integrationsintervall indem er örtliche Unterintervalle hervorruft, deren Länge durch ein neues System überwacht wird. Die Überwachung ergibt sich aus einer Formel, die von einer analytischen Basis abgeleitet wird und für jede beliebige Integrationsregel gilt: mit zwei verschiedenen Annäherungen eines Integrals wird die Intervallänge berechnet, die notwendig ist, um eine Integralannäherung mit der innerhalb zugelassener Fehlergrenzen notwendigen Genauigkeit zu erreichen. Die daraus entstehende Methode für die Erzeugung der Unterintervalle und eine wirksame Auswahl der Fehlerverteilung unter die Unterintervalle bringen einen selbstanpassenden Algorithmus hervor, der über einen genauen und höchst günstigen Integrationsprozeß verfügt. Darauf wird der besondere Algorithmus betrachtet, der sich mit Hilfe der 6-Punkte-Gauß-Legendre-Integrationsregel ergibt. Außerdem wird er mit den besten unter den anderen Integrationsalgorithmen verglichen.
    Notes: Abstract A new adaptive algorithm for the integration of analytic functions is presented. The algorithm processes the integration interval by generating local subintervals whose length is controlled through a feedback loop. Control is performed by means of a relation derived on an analytical basis and valid for an arbitrary integration rule: two different estimates of an integral are used to compute the interval length necessary to obtain an integral estimate with accuracy within the assigned error bounds. The implied method for local generation of subintervals and an effective assumption of error partition among subintervals give rise to an adaptive algorithm provided with an accurate and very efficient integration process. The particular algorithm obtained by choosing the 6-point Gauß-Legendre integration rule is considered and extensive comparisons are made with other outstanding integration algorithms.
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    Zur praktischen Behandlung linearer diskreter Approximationsprobleme in der Maximumsnorm (1978)
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    Computing 21 (1978), S. 37-52 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract Direct methods for the solution of linear approximation problems tend to fail in practice because of numerical instabilities. Difficulties arise from an undesired accumulation of round-off errors. In [3] and in chapter 2 of this paper effective and inexpensive tests are developed to recognize numerical difficulties and stabilize numerical methods by iterative refinement and restart procedures, if necessary. On the ground of this, a stabilized version of a modified revised dual simplex algorithm can be developed capable of solving the approximation problems under consideration. The technical details of this method and a FORTRAN implementation are given in [4]. Numerical examples are discussed to illustrate that the developed method is superior to commonly used algorithms not only by a broader range of applications and more stability, but also by considerably less storage requirement (for large problems), while the execution times are comparable or less.
    Notes: Zusammenfassung Anhäufungen von Rundungsfehlern führen in der Praxis häufig dazu, daß direkte simplexartige Methoden zur Lösung linearer Approximationsprobleme in der Maximumsnorm versagen. Vor dem approximationstheoretischen Hintergrund des Problems werden in der vorliegenden Arbeit einfach durchzuführende Tests entwickelt, die numerische Schwierigkeitenim voraus anzeigen und so Gegenmaßnahmen ermöglichen. Anhand einer Reihe von Beispielen werden Stabilität, Anwendungsbereich und Grenzen darauf aufbauender Algorithmen diskutiert.
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    Algorithm 37 Algorithm for the solution of the 0–1 single knapsack problem (1978)
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    Computing 21 (1978), S. 81-86 
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Für das „0–1 single Knapsack Problem” wird eine FORTRAN-Implementierung eines wirkungsvollen Lösungsverfahrens angegeben. Die angeführten Rechenergebnisse zeigen, daß die vorgeschlagene Methode den derzeit besten bekannten Algorithmen überlegen ist.
    Notes: Abstract The FORTRAN implementation of an efficient algorithm which solves the 0–1 single knapsack problem is given. Computational results are presented, showing the proposed method to be generally superior to the best known algorithms.
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    A new kind of combinations between the Ritz-Galerkin and finite element methods for singularity problems (1988)
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    Computing 40 (1988), S. 29-50 
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    ISSN: 1436-5057
    Keywords: Primary 65N10 ; 65N30 ; Elliptic problems ; singularity problems ; finite element methods ; Ritz-Galerkin methods ; combined methods ; nonconforming combinations ; penalty combined methods ; simplified hybridcombined methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es werden Koppelungstechniken zwischen der Ritz-Galerkin- und der Lagrange-Finite-Elemente-Methode der Ordnungk≥1 vorgestellt, die aus einer Kombination von hybriden Techniken und Straffunktionstechniken bestehen. Mit ihrer Hilfe werden komplizierte Probleme bei homogenen und inhomogenen elliptischen Gleichungen gelöst, insbesondere mit Singularitäten oder auf unbeschränkten Bereichen. Für die numerischen Lösungen werden optimale Konvergenzraten in Sobolev-Normen bewiesen. Diese theoretischen Ergebnisse werden in numerischen Experimenten für die singuläre Motz-Gleichung verifiziert.
    Notes: Abstract The coupling techniques of simplified hybrid plus penalty functions are first presented for matching the Ritz-Galerkin method and thek(k〉-1)-order Lagrange finite element methods to solve complicated problems of elliptic equations, homogeneous or nonhomogeneous, in particular with singularities or unbounded domains. Optimal convergence rates of numerical solutions have been proved in the Sobolev norms. Moreover, the theoretical results obtained in this paper have been verified by numerical experiments for the singular Motz problem.
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    Bit serial addition trees and their applications (1988)
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    Computing 40 (1988), S. 9-17 
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    ISSN: 1436-5057
    Keywords: B.5.1 [Register-Transfer-Level Implementation] Design-Arithmetic and logic units ; B.6.1 [Logic Design]: Design styles-Parallel circuits ; F.2.0. [Analysis of Algorithms and Problem Complexity]: General ; Algorithms ; Parallel algorithm ; logical circuit ; binary integer ; bit serial ; addition ; multiplication ; matrix multiplication ; selection ; sorting ; statistical computations
    Source: Springer Online Journal Archives 1860-2000
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    Description / Table of Contents: Zusammenfassung Wir untersuchen parallele Algorithmen für eine Anzahl von grundlegenden Rechenproblemen. Alle Algorithmen besitzen als Grundoperation die Additionk-stelliger Binärzahlen. Für jedes Problem geben wir die Lösung in Form eines logischen Schaltkreises, für den das Produkt aus Rechenzeit und Anzahl der benutzten Gatter kleiner ist als bei den besten bisher bekannten Algorithmen.
    Notes: Abstract Parallel algorithms are examined for a number of fundamental computational problems. All algorithms have as a basic operation the addition ofk-bit integers. For each problem we present a solution in the form of a logical circuit for which the product of the computation time and number of gates used is smaller than that of the best previously known algorithm.
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    On the convergence of a rule by Monegato for the numerical evaluation of Cauchy principal value integrals (1988)
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    Computing 40 (1988), S. 67-74 
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    ISSN: 1436-5057
    Keywords: Primary 65D30 ; Cauchy principal value integral ; quadrature rules ; convergence ; Legendre polynomials
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In dieser Arbeit wird die Konvergenz einer von G. Monegato eingeführten Interpolations-Quadraturformel für die Auswertung Cauchyscher Hauptwertintegrale untersucht. Die Autoren geben ein Konvergenztheorem für eine große Klasse von Funktionen an sowie Abschätzungen für das Restglied.
    Notes: Abstract In this paper the authors examine the convergence of an interpolatory type quadrature rule proposed by G. Monegato for the evaluation of Cauchy principal value integrals. A convergence theorem is given for a large class of functions and some estimates of the remainder are established.
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    On multivariate interpolation by generalized polynomials on subsets of grids (1988)
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    Computing 40 (1988), S. 201-215 
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    ISSN: 1436-5057
    Keywords: 65D05 ; 41A05 ; Multivariate Hermite interpolation ; multivariate generalized divided differences ; multivariate generalized polynomials
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Man kann diese Note als eine Ergänzung zu einem Aufsatz von H. Werner [17] ansehen, der die klassische Newtonsche Interpolationsformel auf die Hermite-Interpolation mit algebraischen Polynomen in mehreren reellen Veränderlichen auf gewissen Gitter-Teilmengen übertragen hat. Hier werden verallgemeinerte Polynome in mehreren reellen oder komplexen Variablen betrachtet. Es werden rekursive Berechnungsmethoden entwickelt, die die Interpolation mit verallgemeinerten Polynomen in mehreren Variablen ähnlich einfach durchführbar machen wie die mit algebraischen Polynomen. Verallgemeinerte Polynome, die im allgemeinen dieselbe Approximationsgüte wie algebraische Polynome aufweisen, können für spezielle Situationen besser geeignet sein als jene. Insbesondere sind die Ergebnisse dieser Note dazu verwendbar, um nicht-polynomiale finite Elemente zu konstruieren, da in diesem Falle die Interpolationspunkte gewöhnlich regelmäßige Teilsysteme von Gittern bilden. Obwohl der Rahmen dieser Note allgemeiner ist als in [17], sind einige der hier gegebenen Beweise einfacher. Als eine alternative Berechnungsmethode für verallgemeinerte Interpolationspolynome auf Rechtecksgittern wird ein Neville-Aitken-Algorithmus vorgestellt.
    Notes: Abstract This note may be regarded as a complement to a paper of H. Werner [17] who has carried over Newton's classical interpolation formula to Hermite interpolation by algebraic polynomials of several real variables on certain subsets of grids. Here generalized polynomials of several real or complex variables are treated. Recursive procedures are presented showing that interpolation by generalized multivariate polynomials is performed nearly as simply as interpolation by algebraic polynomials. Having in general the same approximation power, generalized polynomials may be better adapted to special situations. In particular, the results of this note can be used for constructing nonpolynomial finite elements since in that case the interpolation points usually are rather regular subsystems of grids. Though the frame is more general than in [17] some of our proofs are simpler. As an alternative method to evaluate multivariate generalized interpolation polynomials for rectangular grids a Neville-Aitken algorithm is presented.
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    Editorial (1988)
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    AI & society 2 (1988), S. 1-1 
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    ISSN: 1435-5655
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    Topics: Computer Science
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    The social shaping of technology and work: Human centred CIM systems (1988)
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    AI & society 2 (1988), S. 47-61 
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    ISSN: 1435-5655
    Keywords: social shaping ; human centred systems ; computer integrated manufacturing ; multidisciplinary design
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This paper decribes the theoretical and methodological issues involved in the social shaping of technology and work, with particular reference to human centred computer integrated manufacturing (CIM) systems. Conventional approaches to the understanding and shaping of the relationship between technology, work and human development are criticised, and an alternative, human centred approach is outlined. The methods and processes whereby the design of human centred CIM systems may be shaped and evaluated are then described and appraised.
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    The application of AI to law (1988)
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    AI & society 2 (1988), S. 31-46 
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    ISSN: 1435-5655
    Keywords: artificial intelligence ; expert systems ; legal practice ; computerisation ; judicial interpretation ; legal ideology ; legal sociology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract There is much interest in moving AI out into real world applications, a move which has been encouraged by recent funding which has attempted to show industry and commerce can benefit from the Fifth Generation of computing. In this article I suggest that the legal application area is one which is very much more complex than it might — at first sight — seem. I use arguments from the sociology of law to indicate that the viewing of the legal system as simply a rule-bound discipline is inherently nave. This, while not new in jurisprudence, is — as the literature of AI and law indicates — certainly novel to the field of artificial intelligence. The socio-legal argument provided is set within the context of AI as one more example of the failure of scientific success and method to easily transmit itself over into the social sciences.
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    Open forum (1988)
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    AI & society 2 (1988), S. 63-78 
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    News section (1988)
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    AI & society 2 (1988), S. 83-93 
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    Artificial intelligence: A contribution to systems theories of sociology (1988)
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    AI & society 2 (1988), S. 113-120 
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    Keywords: artificial intelligence ; sociology ; expert systems ; systemic sociology ; social interaction ; human-machine interaction
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    Notes: Abstract The aim of my contribution is to try to analyse some points of similarity and difference between post-Parsonian social systems theory models for sociology — with special reference to those of W. Buckley, F.E. Emery and N. Luhmann — and expert systems models1 from Artificial Intelligence. I keep specifically to post-Parsonian systems theories within sociology because they assume some postulates and criteria derived from cybernetics and which are at the roots of AI. I refer in particular to the fundamental relevance of the system-environment relationship in both sociology and AI.
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    Human-oriented and machine-oriented reasoning: Remarks on some problems in the history of Automated Theorem Proving (1988)
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    AI & society 2 (1988), S. 121-131 
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    Keywords: human-machine interaction ; automated theorem proving ; mathematical proofs ; reasoning ; sociology of knowledge ; tacit knowledge
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    Notes: Abstract Examples in the history of Automated Theorem Proving are given, in order to show that even a seemingly ‘mechanical’ activity, such as deductive inference drawing, involves special cultural features and tacit knowledge. Mechanisation of reasoning is thus regarded as a complex undertaking in ‘cultural pruning’ of human-oriented reasoning. Sociological counterparts of this passage from human- to machine-oriented reasoning are discussed, by focusing on problems of man-machine interaction in the area of computer-assisted proof processing.
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    Machine intelligence and the long-term future of the human species (1988)
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    AI & society 2 (1988), S. 133-139 
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    Keywords: human intelligence ; machine intelligence ; cultural evolution ; human brain ; electronic systems ; social implications
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    Notes: Abstract Intelligence is not a property unique to the human brain; rather it represents a spectrum of phenomena. An understanding of the evolution of intelligence makes it clear that the evolution of machine intelligence has no theoretical limits — unlike the evolution of the human brain. Machine intelligence will outpace human intelligence and very likely will do so during the lifetime of our children. The mix of advanced machine intelligence with human individual and communal intelligence will create an evolutionary discontinuity as profound as the origin of life. It will presage the end of the human species as we know it. The question, in the author's view, is not whether this will happen, but when, and what should be our response.
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    The Teflon tendency rides again! (1988)
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    AI & society 2 (1988), S. 152-152 
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    Book reviews (1988)
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    AI & society 2 (1988), S. 172-177 
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    News section (1988)
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    AI & society 2 (1988), S. 178-182 
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    Editorial (1988)
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    AI & society 2 (1988), S. 183-183 
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    Knowledge-based systems and issues of integration: A commercial perspective (1988)
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    AI & society 2 (1988), S. 209-233 
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    Notes: Abstract Commercial applications of knowledge-based systems are changing from an embryonic to a growth business. Knowledge is classified by levels and types to differentiate various knowledge-based systems. Applications are categorized by size, generic types, and degree of intelligence to establish a framework for discussion of progress and implications. A few significant commercial applications are identified and perspectives and implications of these and other systems are discussed. Perspectives relate to development paths, delivery modes, types of integration, and resource requirements. Discussion includes organizational opportunities and impacts, business perspectives, workplace issues, public effects, and educational needs. Common traps and modes of failures are mentioned. Major conclusions point to the great value of knowledge-based systems when development is pursued correctly, and to the existence of insufficient understanding of resource requirements, needs for integration, different talents, and incorporation into operational strategy to equitably exploit the significant economic and social costs associated with their creation and use.
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    Computerised manufacturing and empirical knowledge (1988)
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    AI & society 2 (1988), S. 235-243 
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    Keywords: skill-based manufacturing ; human-centred manufacturing ; empirical knowledge ; sensorial perception ; computer-based manufacturing
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    Notes: Abstract What skills are required for working with computer-controlled machines in the manufacturing area? Taking the developments in the machine building sector in Germany as an example, it becomes apparent that a human-centred approach (skill-based manufacturing) offers the companies many advantages over Tayloristic forms of work organisation and automation. Closer observations reveal that skills and qualifications based on empirical knowledge and individual capabilities, such as a feeling for machines and materials, continue to play an important part in the work with computer-controlled machines. So far, however, skills of this kind have received neither practical nor systematic consideration and are regarded as tacit skills in most cases. Therefore it is particularly the use of computer technology which is likely — in most cases unintentionally — to restrict and undermine the essential preconditions necessary for the development and application of such skills.
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    Keep on trukking (1988)
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    AI & society 2 (1988), S. 257-257 
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    The closed world: Systems discourse, military strategy and post WWII American historical consciousness (1988)
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    AI & society 2 (1988), S. 245-255 
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    Keywords: artificial intelligence ; computer systems ; military systems ; SAGE ; SCI ; SDI ; strategy ; discourse ; systems
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    Notes: Abstract This essay proposes a cultural and historical explanation for the American Military's fascination with computing. Three key elements of post-WWII US political culture — apocalyptic struggle with the USSR, subsuming all other conflicts: a long history of antimilitarist sentiment in American politics; and the rise of science-based military power — contributed to a sense of the world as a closed system accessible to American technological control. A developing scientific systems discourse, centrally including computer science and AI, was adopted for strategic thinking and military technology. The Strategic Computing and Strategic Defense Initiatives are discussed as contemporary examples of this conjunction.
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    Editorial (1988)
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    AI & society 2 (1988), S. 277-278 
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    Seeing and seeing-AS (1988)
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    AI & society 2 (1988), S. 303-313 
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    Keywords: perception ; seeing ; seeing-as ; natural reaction ; interpretation
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    Notes: Abstract This paper highlights the importance of inter-relationships between language, context, practice and interpretation. These inter-relationships should be of interest to AI researchers working in multi-disciplinary fields such as knowledge based systems, speech and vision. Attention is drawn to the importance of Part II, Section II of Wittgenstein'sPhilosophical Investigations for understanding the enormous complexity of the concept of seeing and how it is woven into an understanding of language and of human relations.
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    Rule following and tacit knowledge (1988)
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    AI & society 2 (1988), S. 287-301 
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    Keywords: logical positivism ; rule-following ; tacit knowledge ; expert knowledge ; linguistic knowledge ; scientific knowledge ; practice
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    Notes: Abstract This paper discusses the interrelationship between wisdom, science and craft from the perspective of the Wittgenstein concept of tacit knowledge. It challenges the notion of the ‘rules-model’ as put forward by Logical Positivists, and shows the limitation of this model for describing the tacit dimension of knowledge. The paper demonstrates the crucial role of practice in ‘rule-following’ in the real world. It is held that ‘to follow a rule’ is to practice a custom, a usage or an institutional practice. Hence, rules can only exist as a link in social life. The dream of the ‘precise’ language can only be realised in a closed scientific world. It is inadequate for reflecting the user's relationship to language and its content and practice in varied ‘use situations’. It is only through examples that we learn to deal with, describe, interpret and learn from the new situations. The rule-based models which are used to acquire and describe human knowledge in syntactic and propositional forms are, in effect, an impoverishment of the description of reality. It is argued that expert knowledge and linguistic knowledge are linked together and emerge as two sides of the same subject as the pragmatic perspective of reality. The tacit dimension of expert knowledge is, in many cases, more significant than the linguistic knowledge, especially in the case of the vocational and aesthetic world. The challenge to AI researchers, therefore, is to recognise that knowledge based systems which ignore the tacit dimension of expert knowledge not only distance the user from reality but also impoverish the learning process itself.
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    Cheep! Cheep! (1988)
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    AI & society 2 (1988), S. 355-355 
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    Product creation: An appropriate coupling of human and artificial intelligence (1988)
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    AI & society 2 (1988), S. 341-353 
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    Keywords: artificial intelligence ; design ; manufacturing ; human-centred
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    Notes: Abstract Small batch manufacture dominates the manufacturing sector of a growing number of industrialised countries. The organisational structures and management methods currently adopted in such enterprises are firmly based upon historical developments which started with individual craftsmen. These structures and methods are primarily concerned with the co-ordination of human activities, rather than with the management of theknowledge process underlying the creation of products. This paper argues that it is the failure to understand this knowledge process and its effective integration at aKnowledge Level which presents the real barrier to increased flexibility, not, as is presently perceived, a lack of suitableInformation Level integration. Potential techniques and methodologies for achievingKnowledge Level integration are beginning to emerge from Artificial Intelligence research. Realisation of full Knowledge Level integration will not only require further research into the AI techniques and methodologies involved, but also an understanding of the wider human aspects of their application. Some questions concerning the effective coupling of human and artificial intelligence to achieve Knowledge Level integration of the product creation process are presented.
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    A developmental pattern of artificial intelligence based on the blend of man and machine (1988)
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    AI & society 2 (1988), S. 356-360 
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    Pathologies of AI: Responsible use of artificial intelligence in professional work (1988)
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    AI & society 2 (1988), S. 3-16 
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    Keywords: AI paradigm ; knowledge ; semantics ; complexity ; responsibility ; collaboration ; law
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    Topics: Computer Science
    Notes: Abstract Although the AI paradigm is useful for building knowledge-based systems for the applied natural sciences, there are dangers when it is extended into the domains of business, law and other social systems. It is misleading to treat knowledge as a commodity that can be separated from the context in which it is regularly used. Especially when it relates to social behaviour, knowledge should be treated as socially constructed, interpreted and maintained through its practical use in context. The meanings of terms in a knowledge-base are assumed to be references to an objective reality whereas they are instruments for expressing values and exercising power. Expert systems that are not perspicuous to the expert community will lose their meanings and cease to contain genuine knowledge, as they will be divorced from the social processes essential for the maintenance of both meaning and knowledge. Perspicuity is usually sacrificed when knowledge is represented in a formalism, with the result that the original problem is compounded with a second problem of penetrating the representation language. Formalisms that make business and legal problems easier to understand are one essential research goal, not only in the quest for intelligent machines to replace intelligent human beings, but also in the wiser quest for computers to support collaborative work and other forms of social problem solving.
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    Book review (1988)
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    AI & society 2 (1988), S. 79-82 
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    Editorial (1988)
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    AI & society 2 (1988), S. 95-97 
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    The socratic and platonic basis of cognitivism (1988)
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    AI & society 2 (1988), S. 99-112 
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    Keywords: Artificial Intelligence ; checker program ; chess ; cognitivism ; connectionism ; expertise ; expert systems ; heuristic knowledge ; phenomenology ; Physical Symbol System ; Plato ; skill acquisition ; Socrates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Artificial Intelligence, and the cognitivist view of mind on which it is based, represent the last stage of the rationalist tradition in philosophy. This tradition begins when Socrates assumes that intelligence is based on principles and when Plato adds the requirement that these principles must be strict rules, not based on taken-for-granted background understanding. This philosophical position, refined by Hobbes, Descartes and Leibniz, is finally converted into a research program by Herbert Simon and Allen Newell. That research program is now in trouble, so we must return to its source and question Socrates' assumption that intelligence consists in solving problems by following rules, and that one acquires the necessary rules by abstracting them from specific cases. A phenomenological description of skill acquisition suggests that the acquisition of expertise moves in just the opposite direction: from abstract rules to particular cases. This description of expertise accounts for the difficulties that have confronted AI for the last decade.
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    ITS: ‘Invisible tutorial systems’? (1988)
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    AI & society 2 (1988), S. 151-152 
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