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  • 2010-2014
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  • Articles  (6,784)
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  • 2010-2014
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  • 1975-1979  (6,784)
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  • 1
    Electronic Resource
    Electronic Resource
    Explicit duality for convex homogeneous programs (1976)
    Springer
    Mathematical programming 10 (1976), S. 176-191 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract When all the functions that define a convex program are positively homogeneous, then a dual convex program can be constructed which is defined in terms of the primal data only (the primal variables do not appear). Furthermore, the dualizing process, carried out on the dual program, yields the primal. Several well-known examples of convex programs with explicit duals are shown to be special cases.
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    URL: http://dx.doi.org/10.1007/BF01580666
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  • 2
    Electronic Resource
    Electronic Resource
    Optimized relative step size random searches (1976)
    Springer
    Mathematical programming 10 (1976), S. 230-244 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract New results concerning the family of random searches as proposed by Rastrigin are presented. In particular, the random search with reversals and two optimized relative step size random searches are investigated. Random searches with reversals are found to be substantially better than their counterparts. A new principle of updating the step size for this family of searches is proposed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580669
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  • 3
    Electronic Resource
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    On generalizing shapley's index theory to labelled pseudomanifolds (1976)
    Springer
    Mathematical programming 10 (1976), S. 245-262 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract For a bimatrix game one may visualize two bounded polyhedronsX andY, one for each player. OnX × Y one may visualize, as a graphG, the set of almost-complementary points (see text). $$\bar G$$ consists of an even number of nodes, one for each complementary point (one for the origin, others corresponding to extreme points which are equilibrium points); arcs (extreme point paths of almost complementary points); and possibly loops (paths with no equilibrium points). Shapley has shown that one may assign indices (+) and (−) to nodes, and directions called (+) and (−) to arcs or loops in such a way that, leaving a (+) node one moves always in a (+) direction, terminating at a (−) node. Indices and directions for a point are determined knowing only the point. In this paper, these concepts are generalized to labelled pseudomanifolds. An integer labelling of the vertices identifies theG-set of almost-completely labelled simplexes. It is shown that in order for theG-set of any labelling to be directed as above it is necessary and sufficient that the pseudomanifold be orientable. Realized examples for situations of current interest are also developed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580670
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  • 4
    Electronic Resource
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    On triangulations for computing fixed points (1976)
    Springer
    Mathematical programming 10 (1976), S. 322-346 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper introduces theoretical measures of efficiency for triangulations used in computing fixed points. The measures, for both regular triangulations ofR n and those with continuous refinement of grid size, are based on an average count of the number of simplices met by straight line segments. The computation of these measures is facilitated by a description of the facets as well as the vertices of a triangulation. We give a simple description of a modification of Eaves' and Saigal's K3 and compute the measures of efficiency of three regular triangulations ofR n and two triangulations of (0, 1] ×R n with continuous refinement of grid size, including the modified K3.
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    URL: http://dx.doi.org/10.1007/BF01580679
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  • 5
    Electronic Resource
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    Integer programming approaches to the travelling salesman problem (1976)
    Springer
    Mathematical programming 10 (1976), S. 367-378 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The availability of an LP routine where we can add constraints and reoptimize, makes it possible to adopt an integer programming approach to the travelling-salesman problem. Starting with some of the constraints that define the problem we use either a branching process or a cutting planes routine to eliminate fractional solutions. We then test the resulting integer solution against feasibility and if necessary we generate the violated constraints and reoptimize until a “genuine” feasible solution is achieved. Usually only a small number of the omitted constraints is generated. The generality of the method and the modest solution times achieved leads us to believe that such an LP approach to other combinatorial problems deserves further consideration.
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    URL: http://dx.doi.org/10.1007/BF01580682
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  • 6
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    Mathematical programming study 4 (1976)
    Springer
    Mathematical programming 10 (1976), S. 409-412 
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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/BF01580687
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  • 7
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    Convergence conditions for restarted conjugate gradient methods with inaccurate line searches (1976)
    Springer
    Mathematical programming 10 (1976), S. 32-51 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Convergence properties of restarted conjugate gradient methods are investigated for the case where the usual requirement that an exact line search be performed at each iteration is relaxed. The objective function is assumed to have continuous second derivatives and the eigenvalues of the Hessian are assumed to be bounded above and below by positive constants. It is further assumed that a Lipschitz condition on the second derivatives is satisfied at the location of the minimum. A class of descent methods is described which exhibitn-step quadratic convergence when restarted even though errors are permitted in the line search. It is then shown that two conjugate gradient methods belong to this class.
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    URL: http://dx.doi.org/10.1007/BF01580652
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  • 8
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    Feasible directions algorithms for optimization problems with equality and inequality constraints (1976)
    Springer
    Mathematical programming 11 (1976), S. 67-80 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper two algorithms, of the feasible-directions and dual feasible-directions type, are presented for optimization problems with equality and inequality constraints. An associated problem, having only inequality constraints, is defined, and shown to be equivalent to the original problem if a certain parameter is sufficiently large. The algorithms solve the associated problem, but incorporate a method for automatically increasing this parameter in order to ensure global convergence to a solution to the original problem. Any feasible directions algorithm can be similarly modified to enable it to handle equality constraints.
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    URL: http://dx.doi.org/10.1007/BF01580371
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  • 9
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    Superlinearly convergent variable metric algorithms for general nonlinear programming problems (1976)
    Springer
    Mathematical programming 11 (1976), S. 263-282 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper sufficient conditions for local and superlinear convergence to a Kuhn—Tucker point are established for a class of algorithms which may be broadly defined and comprise a quadratic programming algorithm for repeated solution of a subproblem and a variable metric update to develop the Hessian in the subproblem. In particular the DFP update and an update attributed to Powell are shown to provide a superlinear convergent subclass of algorithms provided a start is made sufficiently close to the solution and the initial Hessian in the subproblem is sufficiently close to the Hessian of the Lagrangian at this point.
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    URL: http://dx.doi.org/10.1007/BF01580395
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  • 10
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    The Mathematical Programming Society (1976)
    Springer
    Mathematical programming 11 (1976), S. 301-301 
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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/BF01580399
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  • 11
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    The 8th IFIP Conference on optimization techniques (1976)
    Springer
    Mathematical programming 11 (1976), S. 199-199 
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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/BF01580387
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  • 12
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    Editor's note (1976)
    Springer
    Mathematical programming 11 (1976), S. 203-203 
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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/BF01580390
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  • 13
    Electronic Resource
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    An existence theorem for solutions tof(x) = 0 (1976)
    Springer
    Mathematical programming 11 (1976), S. 252-262 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract InR 1, if a continuous function has opposite signs at the endpoints of an interval, then the function has a zero in the interval. If the function has a nonvanishing derivative at a zero, then there is an interval such that the function has opposite signs at the endpoints. In this paper each of these results is extended toR n .
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    URL: http://dx.doi.org/10.1007/BF01580394
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  • 14
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    Fractional programming without differentiability (1976)
    Springer
    Mathematical programming 11 (1976), S. 283-290 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The notion of quasi-differentiability is examined and related to fractional programming. Necessary and sufficient conditions are given and various other properties of quasi-differentiable functions are discussed. Differentiability is not assumed.
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    URL: http://dx.doi.org/10.1007/BF01580396
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  • 15
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    Projections in minimax algebra (1976)
    Springer
    Mathematical programming 10 (1976), S. 111-123 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract An axiomatic theory of linear operators can be constructed for abstract spaces defined over (R, ⊕, ⊗), that is over the (extended) real numbersR with the binary operationsx ⊕ y = max (x,y) andx ⊗ y = x + y. Many of the features of conventional linear operator theory can be reproduced in this theory, although the proof techniques are quite different. Specialisation of the theory to spaces ofn-tuples provides techniques for analysing a number of well-known operational research problems, whilst specialisation to function spaces provides a natural formal framework for certain familiar problems of approximation, optimisation and duality.
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    URL: http://dx.doi.org/10.1007/BF01580656
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  • 16
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    Council of the Mathematical Programming Society (1976)
    Springer
    Mathematical programming 10 (1976), S. 137-137 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
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  • 17
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    Editorial policy (1976)
    Springer
    Mathematical programming 10 (1976), S. 144-144 
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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/BF01580663
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  • 18
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    A set of geometric programming test problems and their solutions (1976)
    Springer
    Mathematical programming 10 (1976), S. 192-213 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper attempts to provide a set of standard test examples for researchers working in the area of geometric programming and general nonlinear, continuous, nonconvex programming algorithms. The examples consist partly of applications of nonlinear programming that have appeared in the literature and partly of original geometric programming applications. Solutions to all the problems are provided as well as the starting points from which these solutions were computed. Other computationally important aspects such as tolerances and degree of accuracy with which these problems were solved, are also included.
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    URL: http://dx.doi.org/10.1007/BF01580667
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  • 19
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    Analytical solution of A dynamic transaction flow problem (1976)
    Springer
    Mathematical programming 10 (1976), S. 214-229 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We analyze a mathematical programming model of a fractional flow process which consists ofn sectors and all possible time-dependent streams of flow between, into and out of the sectors. Assuming specific constraints on flow, least cost policies are determined for control of the system transactions involved over a given finite time horizon and over an infinite horizon. Several applications of the model are presented and discussed.
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    URL: http://dx.doi.org/10.1007/BF01580668
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  • 20
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    Quadratic duality over convex cone domains (1976)
    Springer
    Mathematical programming 10 (1976), S. 277-283 
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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/BF01580673
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  • 21
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    On A characterization of optimality in convex programming (1976)
    Springer
    Mathematical programming 11 (1976), S. 81-88 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Necessary and sufficient conditions for optimality are given, for convex programming problems, without constraint qualification, in terms of a single mathematical program, which can be chosen to be bilinear.
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  • 22
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    A note on polyhedral sets having A least element (1976)
    Springer
    Mathematical programming 11 (1976), S. 94-96 
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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/BF01580374
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  • 23
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    Finding the nearest point in A polytope (1976)
    Springer
    Mathematical programming 11 (1976), S. 128-149 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A terminating algorithm is developed for the problem of finding the point of smallest Euclidean norm in the convex hull of a given finite point set in Euclideann-space, or equivalently for finding an “optimal” hyperplane separating a given point from a given finite point set. Its efficiency and accuracy are investigated, and its extension to the separation of two sets and other convex programming problems described.
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    URL: http://dx.doi.org/10.1007/BF01580381
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  • 24
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    Transversal matroid intersections and related packings (1976)
    Springer
    Mathematical programming 11 (1976), S. 164-176 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Network flow techniques are used to show that a conjecture of Fulkerson on the blocking polyhedron associated with the intersection of two matroids is true for transversal matroids. This leads to some general integral packing results for partial transversals, bipartite edge matchings, and subpermutation matrices. A computational example for bipartite edge matchings is included.
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    URL: http://dx.doi.org/10.1007/BF01580384
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  • 25
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    Editorial policy (1976)
    Springer
    Mathematical programming 11 (1976), S. 201-201 
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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/BF01580389
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  • 26
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    A dual algorithm for the one-machine scheduling problem (1976)
    Springer
    Mathematical programming 11 (1976), S. 229-251 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A branch and bound algorithm is presented for the problem of schedulingn jobs on a single machine to minimize tardiness. The algorithm uses a dual problem to obtain a good feasible solution and an extremely sharp lower bound on the optimal objective value. To derive the dual problem we regard the single machine as imposing a constraint for each time period. A dual variable is associated with each of these constraints and used to form a Lagrangian problem in which the dualized constraints appear in the objective function. A lower bound is obtained by solving the Lagrangian problem with fixed multiplier values. The major theoretical result of the paper is an algorithm which solves the Lagrangian problem in a number of steps proportional to the product ofn 2 and the average job processing time. The search for multiplier values which maximize the lower bound leads to the formulation and optimization of the dual problem. The bounds obtained are so sharp that very little enumeration or computer time is required to solve even large problems. Computational experience with 20-, 30-, and 50-job problems is presented.
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  • 27
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    Bottleneck linear programming (1976)
    Springer
    Mathematical programming 11 (1976), S. 291-298 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The Bottleneck Linear Programming problem (BLP) is to maximizex 0 = max j c j ,x j 〉 0 subject toAx = b, x ⩾ 0. A relationship between the BLP and a problem solvable by a “greedy” algorithm is established. Two algorithms for the BLP are developed and computational experience is reported.
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  • 28
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    Bicentennial conference on Mathematical Programming (1976)
    Springer
    Mathematical programming 10 (1976), S. 284-284 
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  • 29
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    Editorial policy (1976)
    Springer
    Mathematical programming 10 (1976), S. 286-286 
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  • 30
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    An algorithm for nonconvex programming problems (1976)
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    Mathematical programming 10 (1976), S. 312-321 
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    ISSN: 1436-4646
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    Topics: Computer Science , Mathematics
    Notes: Abstract Branch and bound approaches for nonconvex programming problems had been given in [1] and [4]. Crucial for both are the use of rectangular partitions, convex envelopes and separable nonconvex portions of the objective function and constraints. We want to propose a similar algorithm which solves a sequence of problems in each of which the objective function is convex or even linear. The main difference between this approach and previous approaches is the use of general compact partitions instead of rectangular ones and a different refining rule such that the algorithm does not rely on the concept of convex envelopes and handles non-separable functions. First we describe a general algorithm and prove a convergence theorem under suitable regularity assumptions. Then we give as example an algorithm for concave minimization problems.
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  • 31
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    Quasi balanced matrices — An addendum (1976)
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    Mathematical programming 10 (1976), S. 405-407 
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  • 32
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    The Mathematical Programming Society (1976)
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    Mathematical programming 10 (1976), S. 413-413 
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  • 33
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    Optimal conditioning of self-scaling variable Metric algorithms (1976)
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    Mathematical programming 10 (1976), S. 70-90 
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    Notes: Abstract Variable Metric Methods are “Newton—Raphson-like” algorithms for unconstrained minimization in which the inverse Hessian is replaced by an approximation, inferred from previous gradients and updated at each iteration. During the past decade various approaches have been used to derive general classes of such algorithms having the common properties of being Conjugate Directions methods and having “quadratic termination”. Observed differences in actual performance of such methods motivated recent attempts to identify variable metric algorithms having additional properties that may be significant in practical situations (e.g. nonquadratic functions, inaccurate linesearch, etc.). The SSVM algorithms, introduced by this first author, are such methods that among their other properties, they automatically compensate for poor scaling of the objective function. This paper presents some new theoretical results identifying a subclass of SSVM algorithms that have the additional property of minimizing a sharp bound on the condition number of the inverse Hessian approximation at each iteration. Reducing this condition number is important for decreasing the roundoff error. The theoretical properties of this subclass are explored and two of its special cases are tested numerically in comparison with other SSVM algorithms.
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  • 34
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    A cutting plane algorithm for solving bilinear programs (1976)
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    Mathematical programming 11 (1976), S. 14-27 
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    Notes: Abstract This paper addresses itself to a special class of nonconvex quadratic program referred to as a bilinear program in the literature. We will propose here a cutting plane algorithm to solve this class of problems. The algorithm is along the lines of H. Tui and K. Ritter, but it differs in its exploitation of the special structure of the problem. Though the algorithm is not guaranteed at this stage of the research to converge to a global optimum, the preliminary results of numerical experiments are encouraging.
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  • 35
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    Approximate cutting planes in nonlinear programming (1976)
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    Mathematical programming 11 (1976), S. 194-198 
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    Notes: Abstract An approximation criterion is presented and a convergence proof is given that allows adaptation of the cutting plane algorithm when it is impractical to compute the exact cutting planes. A source application is briefly described and a class of functions is presented for which such approximate cutting planes can be conveniently computed.
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  • 36
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    The Mathematical Programming Society (1976)
    Springer
    Mathematical programming 11 (1976), S. 200-200 
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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/BF01580388
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    Errorbounds for simple zeros of λ-matrices (1976)
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    Computing 16 (1976), S. 17-27 
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir beschreiben hier eine Methode, mit der man Fehlerabschätzungen für Eigenwerte und Eigenvektoren von λ-Matrizen erhalten kann. Mit den Ergebnissen aus einer früheren Arbeit des Autors (siehe [11]) wird ein Algorithmus gefunden, der mit wenig Rechenaufwand gute Abschätzungen liefert. Der Algorithmus wird an mehreren Beispielen getestet.
    Notes: Abstract We describe a method for finding errorbounds for eigenvalues und eigenvectors of λ-matrices. Results from an earlier paper by the author (see [11]) are used to find a fast algorithm that produces good errorbounds. The algorithm is tested on several examples.
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    URL: http://dx.doi.org/10.1007/BF02241976
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    A-stability of Runge-Kutta methods with single and multiple nodes (1976)
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    Computing 16 (1976), S. 39-48 
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Die Vermutung von Ehle [5], daß gewisse Klassen von Runge-Kutta-Methoden A-stabil sind, wird bewiesen. Danach werden implizite RK-Methoden mit mehrfachen Knoten („multiderivative methods” [7]) betrachtet, die den Vorteil haben, daß für höhere Ordnung das zu lösende implizite System von wesentlich geringerer Dimension ist. Es wird gezeigt, daß diese Methoden, falls sie auf Gaußscher (Turanscher) Quadratur beruhen, nur A(α)-stabil (α〈π/2) sind. Daher werden anschließend Methoden bestimmt, die auf Lobatto-Quadratur (mit mehrfachen Knoten) basieren und die sich als A-stabil erweisen; ihre Koeffizienten werden angegeben (bis zur Ordnung 22).
    Notes: Abstract This paper gives the proofs of the conjectures of Ehle [5] concerning the A-stability of classes of implicit Runge-Kutta methods. Next the attention is turned to implicit RK methods with multiple nodes (“multiderivative methods” [7]), which have the advantage that, for higher orders, the implicit system to be solved has much lower dimension. These methods, if based on Gaussian (Turan) quadrature, are shown to be A(α)-stable (α〈π/2) only. Thus, in this paper, methods based on Lobatto quadrature (with multiple nodes) are constructed, which turn out to be A-stable. The coefficients are tabulated up to order 22.
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    Numerical solution of the singular Ginzburg-Landau equations by multiple shooting (1976)
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    Computing 16 (1976), S. 61-67 
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird eine handliche Methode zur Lösung singulärer Randwertprobleme gewöhnlicher Differentialgleichungen behandelt. Taylorreihenentwicklungen des Systems in einem kleinen Intervall blenden die Singularität aus, so daß die Aufgabe mit der Mehrzielmethode gelöst werden kann. Die Zuverlässigkeit dieses Verfahrens wird bei der Lösung der Ginzburg-Landau-Gleichungen der Supraleitung nachgewiesen.
    Notes: Abstract A useful method for the numerical solution of singular two-point boundary value problems by multiple shooting techniques is treated. In a small interval Taylor series expansions are used in orderto kill the numerical singularity. The reliability of the method is demonstrated by solving the Ginzburg-Landau equations arising in the theory of superconductivity.
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    An algorithm of optimization for a special class of networks (1976)
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    Computing 16 (1976), S. 77-97 
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    ISSN: 1436-5057
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In dieser Arbeit wird ein Optimierungsalgorithmus für nichtmarkowsche Netze dargestellt. Es wird die Definition des betrachteten Netzes gegeben und ein Optimierungsproblem formuliert. Es werden das allgemeine Konzept und dann das Ablaufschema des Algorithmus dargestellt. Die Realisierung des Algorithmus wird an einem einfachen Beispiel erklärt. Es werden auch die Möglichkeiten der Anwendung des Verfahrens für Allokationsprobleme und für nichtlineare Programmierung erwähnt. Das Programm ist in FORTRAN IV geschrieben. Es ermöglicht die Realisierung des Verfahrens auf einer EDV-Anlage.
    Notes: Abstract In this paper the author presents an algorithm of optimization for a special class of networks not having the Markov property. A definition of the class of networks under consideration and a formulation of the optimization problem are given. A conception of the algorithm is discussed and next the general and detailed flow diagrams of the algorithm are offered. The realization of the algorithm is illustrated with a simple example showing the process of execution of the tasks included in the algorithm. Some possibilities of applying the algorithm in allocation problems and nonlinear integer programming are presented. The computer program in FORTRAN IV for the execution of the algorithm is enclosed.
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    The secand method in banach spaces (1976)
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    Computing 16 (1976), S. 201-209 
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    ISSN: 1436-5057
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es werden Iterationsverfahren zur Bestimmung von Nullstellen nichtlinearer Operatoren in Banach-Räumen behandelt, die mit Steigungen erster Ordnung arbeiten. Zur Berechnung der Steigungen werden die Punkte auf einer Kugel beliebig gewählt.
    Notes: Abstract The paper concerns to solutions of the operator equationf(x)=0. Using the quotient operator the equation is solved with the iteration method. Points from a given sphere are arbitrarily chosen for quotients creating.
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    Approximation von stochastischen Differentialgleichungen auf Digital- und Hybridrechnern (1976)
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    Computing 16 (1976), S. 359-371 
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    Description / Table of Contents: Abstract Continuous dynamical systems which are subject to random disturbances can often be represented by stochastic differential equations of the Itô-type. We discuss methods how to approximate the solution of such equations on digital and hybrid computers. The digital methods are stochastic versions of some simple deterministic methods. We give convergence theorems which show that stochastic methods differ in principle from their corresponding deterministic methods.
    Notes: Zusammenfassung Kontinuierliche dynamische Systeme, die zufälligen Störungen unterworfen werden, lassen sich oft als stochastische Differentialgleichungen vom Itô-Typ darstellen. Wir untersuchen Methoden, durch die die Lösung solcher Gleichungen auf Digital- und Hybridrechnern angenähert werden kann. Die digitalen Verfahren sind stochastische Versionen von einfachen deterministischen Verfahren. Konvergenzsätze zeigen, daß sich stochastische Verfahren prinzipiell von den entsprechenden deterministischen unterscheiden.
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    Untersuchungen des Zeitgewinns durch neue Algorithmen zur Matrix-Multiplikation (1976)
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    Computing 17 (1976), S. 23-36 
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    Topics: Computer Science
    Description / Table of Contents: Abstract This papers gives a survey of possible speed-ups of matrix-multiplication by the methods due to S. Winograd and V. Straßen. Questions of implementation of the algorithms are investigated and formulas for the required additional core-memory are given. By using a machine model which is similar to existing computers the results given are of practical importance.
    Notes: Zusammenfassung Diese Arbeit soll eine Übersicht über den möglichen Zeitgewinn geben, der durch den Einsatz der schnelleren Matrix-Multiplikationen von S. Winograd und V. Straßen erzielbar ist. Implementierungsfragen werden besprochen und der benötigte Zusatzspeicher wird ermittelt. Die Abschätzungen beruhen auf einem Rechner-Modell, welches den heutigen Rechenanlagen nachgebildet ist, und liefern daher realistische Ergebnisse.
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    Über Verfahren zur zweiseitigen Approximation inverser Elemente (1976)
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    Computing 17 (1976), S. 59-67 
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    ISSN: 1436-5057
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    Topics: Computer Science
    Description / Table of Contents: Abstract In a partially ordered ring, a set of iterative methods is constructed in order to approximate the inverse of a given element, not necessarily positive or inverse-positive. Two sequences are generated both converging to the inverse. In addition the inverse is monotonously enclosed. The method of order four has the maximal efficiency index.
    Notes: Zusammenfassung Anknüpfend an Arbeiten von G. Alefeld und J. Herzberger und von J. W. Schmidt werden in einem halbgeordneten RingR Iterationsverfahren untersucht, welche geeignet sind, die Inverse eines nicht notwendig positiven oder inverspositiven Elementesa∈R zu approximieren. Es werden jeweils zwei Folgen (X n ) und (y n ) konstruiert, welche beide gegen die Inversea −1 konvergieren und diese zusätzlich im Sinne vonX n−1 ≦X n ≦a −1 ≦y n ≦y n−1 monoton einschließen. Von den betrachteten Verfahren hat das vierter Ordnung den größten Effektivitätsindex.
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    A method for calculating the reciprocal coefficients of function matrices (1976)
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    Computing 16 (1976), S. 29-37 
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    ISSN: 1436-5057
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird eine allgemeine Methode für die Berechnung der reziproken Reihen zu einer gegebenen Potenzreihe mit Matrizenkoeffizienten vorgeschlagen. Eine ihrer Anwendungen ist für die Inversion einer Matrix, deren Elemente rationale Funktionen sind.
    Notes: Abstract A general method is proposed for calculating the reciprocal series of a given series with matrix coefficients. An application is to the inversion of matrices with entries in the form of rational functions.
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    Monotone switching circuits and boolean matrix product (1976)
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    Computing 16 (1976), S. 99-111 
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    ISSN: 1436-5057
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir untersuchen den Effekt lokaler Änderungen auf das Eingabe/Ausgabe-Verhalten monotoner Netzwerke. Wir wenden die Ergebnisse auf die Multiplikation Boolescher Matrizen an und zeigen, daß die Schulmethode für die Matrizenmultiplikation den alleinigen optimalen Schaltkreis liefert.
    Notes: Abstract We explore the concept of local transformations of monotone switching circuits, i.e. what kind of local changes in a network leave the input/output behavior invariant. We obtain several general theorems in this direction. We apply these results to boolean matrix product and prove that the school-method for matrix multiplication yields the unique monotone circuit.
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    Algorithmus 27 Ein neuer Algorithmus zur Bestimmung vonk-kürzesten Wegen in einem Graphen (1976)
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    Computing 16 (1976), S. 139-151 
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    Description / Table of Contents: Abstract The following algorithm for finding thek-shortest loopless paths from one node to another is a development of the algorithm published in [2]. Though memory need is less, the new algorithm is running is bout 20 times as fast on large networks (1000 nodes and more). The computer time increases linearly withk and about quadratic with the number of nodes on the generated paths.
    Notes: Zusammenfassung Der in der vorliegenden Arbeit vorgestellte Algorithmus zur Ermittlung vonk-kürzesten schleifenfreien Kantenfolgen von einem Anfangsknoten zu einem Endknoten stellt eine Weiterentwicklung des in [2] beschriebenen Verfahrens dar. Bei deutlich geringerem Speicherplatzbedarf konnte die Rechengeschwindigkeit stark gesteigert werden (bei Graphen von 1000 Knoten ungefähr um das 20fache). Die Rechenzeit wächst linear mitk und in etwa quadratisch mit der Knotenzahl der erzeugten Wege.
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    Buchbesprechungen (1976)
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    Computing 16 (1976), S. 169-185 
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    Topics: Computer Science
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    URL: http://dx.doi.org/10.1007/BF02241988
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    Monotone Einschließung von Inversen positiver Elemente durch Verfahren vom Schulz-Typ (1976)
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    Computing 16 (1976), S. 211-219 
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    Description / Table of Contents: Abstract The conditional iterationx n+1 =sup (x n ,x n +x n (e−ax n )),y n−1 =inf (y n ,x n +y n (e−ax n )) generating sequences (x n ) and (y n ) is considered in partially ordered spaces. Under certain conditions it is shown, that the inversea −1 of a positive elementa≧0 is monotonously enclosed in the sensex n ≦x n+1 ≦a −1 ≦y n+1 ≦y n and that (x n ) and (y n ) converge toa −1 quadratically.
    Notes: Zusammenfassung Es wird gezeigt, daß die bedingte Iterationx n+1 =sup (x n ,x n +x n (e−ax n )),y n+1 =inf (y n ,x n +y n (e−ax n )) unter bestimmten Voraussetzungen die Inversea −1 eines positiven Elementsa≧0 gemäßx n ≦x n+1 ≦a −1 ≦y n+1 ≦y n monoton einschließt und daß die Folgen (x n ) und (y n ) quadratisch gegena −1 konvergieren.
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    Boundary flux estimates for elliptic problems by the perturbed variational method (1976)
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    Computing 16 (1976), S. 339-347 
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    ISSN: 1436-5057
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In dieser Arbeit wird gezeigt, daß man scharfe Schranken für die Normalableitung durch die Anwendung eines Extrapolationsprozesses im gestörten Variationsprinzip erhalten kann. QuasioptimaleL 2-Schranken für den Fehler werden angegeben, sowie numerische Resultate in einem Modellproblem.
    Notes: Abstract In this note we show that high order accurate approximations to the boundary flux are readily obtained by use of certain extrapolation process in the perturbed variational principle. QuasioptimalL 2 estimates for the error are obtained. Numerical results are presented for a model problem.
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    On an approach to the automatic evaluation of the subjects' verbal behavior in Roemer's inkblot tests (1976)
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    Computing 16 (1976), S. 373-378 
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    ISSN: 1436-5057
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Roemer, ein Mitarbeiter von Roschach, entwickelte eine „Symboltestserie”, die als eine der projektiven Methoden bei psycho-diagnostischen Tests verwendet wird. (Fragen nach der Verläßlichkeit solcher Methoden stehen hier nicht zur Debatte.) Ein in der Entwicklung stehendes, lernendes Programm wird beschrieben, das Versuchspersonen auf Grund ihres verbalen Verhaltens klassifizieren könnte. Wird das vom Computer gelieferte Persönlichkeitsprofil mit der Diagnose des Psychologen, die als „objektive Wahrheit” angenommen wird, verglichen, so läßt sich seine Qualität laufend verbessern.
    Notes: Abstract Roemer, a collaborator of Rorschach's, devised a “symbol test series” that is used as one of the projective methods of psychodiagnostic testing. We refrain from getting involved in the controversy related to the reliability of such technique. A learning program under development is described that would be able to classify the subjects on the basis of their verbal behavior. By comparing the diagnosis of the psychologist, accepted as “objective truth”, with the profile provided by the computer, the quality of the latter can be made to improve continuously.
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    Ein intergriertes Hardware-Software-System zur Steuerung der Ein/Ausgabe (1976)
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    Computing 17 (1976), S. 1-21 
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    ISSN: 1436-5057
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    Topics: Computer Science
    Description / Table of Contents: Abstract The input/output components in contemporary operating systems are frequently “grown” parts which have individually and specifiquely been designed and amended in the course of new technical developments. However, a rigid analysis reveals the possibility for a unique control system which is mainly built upon the means for interprocess communication. The system is easily continuated into the technical elements. Also, inhomogeneities within the peripheral attachment scheme as well as unconventional service strategies are smoothly incorporated.
    Notes: Zusammenfassung In heutigen realen Betriebssystemen sind die Ein/Ausgabekomponenten häufig „gewachsene” Teile, die im Zuge neuer technischer Ausbauten individuell und spezifisch entworfen und aufgenommen wurden. Bei genauer Analyse ergibt sich die Möglichkeit, ein einheitliches Steuerungssystem zu entwerfen, das im wesentlichen auf die Interprozeßkommunikationsmittel zurückgreift. Dieses System setzt sich zwanglos in die technischen Elemente hinein fort. Es zeigt sich, daß auch Inhomogenitäten im Anschlußschema und besondere Abfertigungsstrategien leicht zu berücksichtigen sind.
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    On the numerical solution of some algebraic integral equations (1976)
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    Computing 17 (1976), S. 69-77 
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    ISSN: 1436-5057
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir behandeln die numerische Lösung einiger algebraischer Integralgleichungen und Integralgleichungen vom Lichtenstein-Typ mit Hilfe einer Variationsmethode und unter Verwendung des Unterraumes derL-Splinefunktionen. Für diese Näherungslösungen werden die Beweise der Existenz, Eindeutigkeit und Konvergenz sowie Fehlerabschätzungen gegeben.
    Notes: Abstract We discuss the numerical solution of some algebraic integral equations and integral equations of Lichtenstein type by means of a variational method and by using the subspace ofL-splines. For these approximate solutions the proofs of existence, uniqueness, and convergence as well as error estimates are given.
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    Parameterdarstellung kubischer und bikubischer Splines (1976)
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    Computing 17 (1976), S. 87-92 
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    Description / Table of Contents: Abstract The known representation of curves and surfaces by P. Bezier is applied to cubic and bicubic splines. In this form spline-conditions are particularly vivid and along easily manageable. A parametric representation naturally connected with spline-conditions allows moreover a most simple and clear correction of splines and bisplines.
    Notes: Zusammenfassung Die bekannte Darstellung von Kurven und Flächen nach Pierre Bezier wird auf kubische und bikubische Splines angewendet. In dieser Darstellung sind die Spline-Bedingungen besonders anschaulich und daher leicht zu handhaben. Eine mit den Spline-Bedingungen auf natürliche Weise verbundene Parameterdarstellung gestattet außerdem eine höchst einfache und übersichtliche Korrektur der Splines und Bisplines.
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    On maximally distant spanning trees of a graph (1976)
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    Computing 17 (1976), S. 115-119 
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    Description / Table of Contents: Zusammenfassung Eine Menge vonk Gerüsten eines GraphenG heißtmaximal entfernt, falls ihre Vereinigung eine maximale Anzahl von Kanten des Graphen enthält. Es wird eine notwendige und hinreichende Bedingung angegeben, die gewährleistet, daß eine Menge von Gerüsten maximal entfernt ist. Dann wird ein effizienter Algorithmus beschrieben, der in einem gegebenen Graphenk maximal entfernte Gerüste findet.
    Notes: Abstract A set ofk spanning trees of a graphG is calledmaximally distant if their union contains the maximum number of edges ofG. We present a necessary and sufficient condition for a set of spanning trees to be maximally distant. We also give an efficient algorithm which actually findsk maximally distant spanning trees in a given graph.
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    Numerische Erfahrungen bei der Lösung des dreidimensionalen Transportproblems (1976)
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    Computing 17 (1976), S. 129-145 
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    Description / Table of Contents: Abstract To find an initial basic feasible solution is a special problem on solving the three dimensional transportation problem. It is not possible to do this work in a similar simple way as it can be done in the usual transportation problem. In [3] Haley proposes to solve a new problem that is essentionally the old one with the addition of a set of artificial variables. However, numerical investigations have shown that this procedure enlarges the amount of computing very much. This paper now gives another procedure for finding an initial basic solution for the three dimensional transportation problem. A great number of examples is discussed which demonstrate the efficiency of this procedure.
    Notes: Zusammenfassung Bei der Lösung eines dreidimensionalen Transportproblems bereitet die Ermittlung einer ersten zulässigen Basislösung Schwierigkeiten, da man nicht mehr so einfach vorgehen kann wie beim gewöhnlichen Transportproblem. In [3] schlägt Haley vor, hierfür ein geeignetes Hilfsproblem zu lösen, das ebenfalls die Form eines dreidimensionalen Transportproblems hat. Nuemrische Untersuchungen haben aber gezeigt, daß dieses Vorgehen einen hohen Rechenaufwand erfordert. In dieser Arbeit wird deshalb eine Alternative zur Ermittlung einer ersten zulässigen Basislösung beim dreidimensionalen Transportproblem angegeben und anhand zahlreicher durchgerechneter Beispiele die größere Effizienz dieses Verfahrens aufgezeigt.
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    Sampling from the poisson distribution on a computer (1976)
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    Computing 17 (1976), S. 147-156 
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    ISSN: 1436-5057
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    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Diese Arbeit beschreibt eine Methode zur Erzeugung von Poissonverteilten Zufallszahlen mit einem Computer, die schneller zu sein scheint als eine in [1] angegebene Methode. Die empfohlene Methode beruht für nichtganzzahlige μ〈7 auf einem konventionellen Suchalgorithmus nach Verwendung der Umkehrtransformation, für ganzzahlige μ auf einer Modifikation davon, wobei die Suche beim Modus beginnt und auf einer Kombination dieser beiden Methoden für nichtganzzahlige μ〉7. Für große μ ist die Rechenzeit proportional zu $$\sqrt \mu $$ . In der Arbeit wird auch gezeigt, daß für μ≥15 bei Verwendung von max (0, [μ + $$Y\sqrt \mu $$ + 0.5]), wobeiY nachN(0, 1) verteilt ist, derselbe Fehler auftritt. Da die Rechenzeit fürY eine Konstante ist, liefert diese Methode eine obere Schranke für die Rechenzeit zur Erzeugung nach Poisson verteilter Zufallszahlen.
    Notes: Abstract This paper describes a method of sampling from the Poisson distribution on a computer that appears to be less costly than a recently suggested method in [1]. The proposed method relies on a conventional search using the inverse transform approach for nonintegral μ〈7, on a modification of the inverse transform approach that begins the search at the mode for integral μ, and on a combination of these two approaches for nonintegral μ〉7. For large μ the sampling cost is proportional to μ1/2. The paper also shows that for μ≥15 an incidental error occurs by using max (0, [μ+Yμ1/2+0.5]) whereY is fromN(0,1). Since the sampling cost ofY is a constant, this approach places an upper bound on the cost of generating a Poisson variate.
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    An integral equation method for the numerical calculation of ion drift and diffusion in evaporated dielectrics (1976)
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    Computing 17 (1976), S. 169-176 
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    Description / Table of Contents: Zusammenfassung Es wird eine Methode vorgelegt, um die partielle Differentialgleichung für einen zeitabhängigen Strömungs-Diffusionsprozeß in einem eindimensionalen endlichen Raum zu lösen. Die Methode beruht auf einer Integralgleichungstechnik, die leicht mit Hilfe von Ziffernrechenanlagen durchgeführt werden kann. Die Technik wurde dazu verwendet, den Transport von beweglichen Ionen in evakuierten Dielectrica unter dem Einfluß eines elektrischen Feldes zu studieren.
    Notes: Abstract A method is presented to solve the partial differential equation for a time dependent drift — diffusion process in a one dimensional finite space. The method is based on an integral equation technique, which is easily solved numerically on a digital computer. This technique has been used to study the transport phenomenon of mobile ions in evaporated dielectrics under influence of an electric field.
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    Zur numerischen Behandlung inkorrekt gestellter aufgaben (1976)
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    Computing 17 (1976), S. 193-206 
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    Description / Table of Contents: Abstract For the numerical solution of improperly posed problems a regularization by linear inqualities is proposed. In order to avoid difficulties with ill-conditioned matrices, the problem is solved by computing certain correct functionals and by singular value decomposition of the matrices.
    Notes: Zusammenfassung Zur numerischen Behandlung von inkorrekt gestellten Problemen wird eine Regularisierung durch Ungleichungen vorgeschlagen. Schweirigkeiten mit schlecht konditionierten Matrizen kann man durch Zurückführen des Problems auf die Berechnung von geeigneten korrekten Funktionalen und durch Zerlegung der Matrizen nach singulären Werten vermeiden.
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    Zur Diskretisierung quasilinearer elliptischer Differentialgleichungen vierter Ordnung (1976)
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    Computing 17 (1976), S. 231-246 
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    Description / Table of Contents: Abstrakt The present paper is concerned with the numerical solution of quasilinear elliptic differential equations of the fourth order by the method of finite differences. A discrete analogue of the corresponding variational problem is constructed. Existence and uniqueness of the solution of the discrete problem and, in connection with the convergence to the exact solution, consistence and stability are treated.
    Notes: Zusammenfassung Quasilineare elliptische Differentialgleichungen vierter Ordnung werden numerisch behandelt mit dem Differenzenverfahren, indem das zugehörige Variationsproblem diskretisiert wird. Existenz und Eindeutigkeit der diskreten Lösung und Konvergenz dieser gegen die exakte Lösung werden bewiesen. In diesem Zusammenhang werden Untersuchungen über Konsistenz und Stabilität angestellt.
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    Some convergence properties of the conjugate gradient method (1976)
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    Mathematical programming 11 (1976), S. 42-49 
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    Notes: Abstract It has been conjectured that the conjugate gradient method for minimizing functions of several variables has a superlinear rate of convergence, but Crowder and Wolfe show by example that the conjecture is false. Now the stronger result is given that, if the objective function is a convex quadratic and if the initial search direction is an arbitrary downhill direction, then either termination occurs or the rate of convergence is only linear, the second possibility being more usual. Relations between the starting point and the initial search direction that are necessary and sufficient for termination in the quadratic case are studied.
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    The assignment polytope (1976)
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    Mathematical programming 11 (1976), S. 97-101 
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    Nominations for Treasurer and Council (1976)
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    Mathematical programming 11 (1976), S. 102-102 
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    A network simplex method (1976)
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    Mathematical programming 11 (1976), S. 105-116 
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    Notes: Abstract Simple combinatorial modifications are given which ensure finiteness in the primal simplex method for the transshipment problem and the upper-bounded primal simplex method for the minimum cost flow problem. The modifications involve keeping “strongly feasible” bases. An efficient algorithm is given for converting any feasible basis into a strongly feasible basis. Strong feasibility is preserved by a rule for choosing the leaving basic variable at each simplex iteration. The method presented is closely related to a new perturbation technique and to previously known degeneracy modifications for shortest path problems and maximum flow problems.
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    Further facet generating procedures for vertex packing polytopes (1976)
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    Mathematical programming 11 (1976), S. 158-163 
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    A dual decomposition algorithm (1976)
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    Mathematical programming 11 (1976), S. 177-193 
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    Notes: Abstract Suppose that a large-scale block-diagonal linear programming problem has been solved by the Dantzig—Wolfe decomposition algorithm and that an optimal solution has been attained. Suppose further that it is desired to perform a post-optimality analysis or a complete parametric analysis on the cost-coefficients or the RHS of the linking constraints. Efficient techniques for performing these analyses for the ordinary simplex case have not been easily applied to this case as one operation involves doing a minimizing ratio between all columns of two rows of the tableau. As the columns are not readily known in Dantzig—Wolfe decomposition, other techniques must be used. To date, suggested methods involve solving small linear programs to find these minimizing ratios. In this paper a method is presented which requires solving no linear programs (except possibly in the case of degeneracy of a subproblem) using and utilizing only the information typically stored for Dantzig—Wolfe decomposition.
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    Concepts of optimality and their uses (1976)
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    Mathematical programming 11 (1976), S. 212-228 
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    On the number of solutions to the linear comple-mentarity problem (1976)
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    Mathematical programming 10 (1976), S. 347-353 
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    Notes: Abstract Given ann × n matrixA and ann-dimensional vectorq letN(A, q) be the cardinality of the set of solutions to the linear complementarity problem defined byA andq. It is shown that ifA is nondegenerate thenN(A, q) + N(A, −q) ⩽ 2 n , which in turn impliesN(A, q) ⩽ 2 n − 1 ifA is also aQ-matrix. It is then demonstrated that min q≠0 N(A, q) ⩽ 2 n−1 − 1, which concludes that the complementary cones cannot spanR n more than 2 n−1 − 1 times around. For anyn, an example of ann × n nondegenerateQ-matrix spanning allR n , but a subset of empty interior, 2[n/3] times around is given.
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    A combinatorial equivalence between A class of multicommodity flow problems and the capacitated transportation problem (1976)
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    Mathematical programming 10 (1976), S. 401-404 
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    Symposium announcement (1976)
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    Mathematical programming 11 (1976), S. 302-302 
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    Sensitivity analysis for nonlinear programming using penalty methods (1976)
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    Mathematical programming 10 (1976), S. 287-311 
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    Notes: Abstract In this paper we establish a theoretical basis for utilizing a penalty-function method to estimate sensitivity information (i.e., the partial derivatives) of a localsolution and its associated Lagrange multipliers of a large class of nonlinear programming problems with respect to a general parametric variation in the problem functions. The local solution is assumed to satisfy the second order sufficient conditions for a strict minimum. Although theoretically valid for higher order derivatives, the analysis concentrates on the estimation of the first order (first partial derivative) sensitivity information, which can be explicitly expressed in terms of the problem functions. For greater clarity, the results are given in terms of the mixed logarithmic-barrier quadratic-loss function. However, the approach is clearly applicable toany algorithm that generates a once differentiable “solution trajectory”.
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    Algorithm 29 efficient algorithms for doubly and multiply restricted partitions (1976)
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    Computing 16 (1976), S. 163-168 
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    Description / Table of Contents: Zusammenfassung Es werden Algorithmen beschrieben zur Konstruktion der Partitionen einer ganzen Zahl in eine vorgeschriebene Anzahl von (verschiedenen oder nicht notwendig verschiedenen) Teilen. Die zugelassenen Teile können aus einem ganzzahligen Intervall oder einer allgemeineren Menge von ganzen Zahlen gewählt werden. Zwei ALGOL-Prozeduren werden angegeben, und einige Resultate diskutiert.
    Notes: Abstract An account is given of algorithms for constructing partitions of an integer into a specified number of parts (with or without the requirement that the parts be distinct). The allowed parts may form a segment or a more general prescribed set of integers. Two ALGOL procedures are given, and some computational results are discussed.
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    Algorithmus 31 Ein Algorithmus zur Bestimmung von Weganzahlen in Netzen (1976)
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    Computing 17 (1976), S. 93-96 
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    Description / Table of Contents: Abstract The current most economical solution to network problems is via Monte Carlo simulation. One of the main problems when using a computer is to answer the question of the storage space required. This depends roughly on the number of paths in the network. Here an algorithm will be presented to compute in a simple manner the number of paths in a network by constructing a sequence of special graphs.
    Notes: Zusammenfassung Die Simulation ist zurzeit wohl das geeignetste Mittel zur Behandlung vieler Probleme der Netzplantechnik. Eines der Hauptprobleme beim Einsatz von Simulationsmethoden ist die Beantwortung der Frage nach der benötigten Speicherkapazität. Duese hängt im wesentlichen von der Anzahl der Wege des Netzes ab. Es wird hier ein Algorithmus angegeben, der auf einfache Weise die Anzahl der Wege in einem Netz zu berechnen gestattet, indem eine spezielle Folge von Graphen konstruiert wird.
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    The NP-Completeness of the bandwidth minimization problem (1976)
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    Computing 16 (1976), S. 263-270 
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    Description / Table of Contents: Zusammenfassung Es wird gezeigt, daß das Problem, die minimale Bandbreite der von Null verschiedenen Elemente einer schwach besetzten symmetrischen Matrix durch Umstellung der Reihen und Spalten zu finden, und einige verwandte Probleme der Kombinatorik NP-geschlossene sind.
    Notes: Abstract The Problem of minimizing the bandwidth of the nonzero entries of a sparse symmetric matrix by permuting its rows and columns and some related combinatorial problems are shown to be NP-Complete.
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    On strongly equivalent context-free grammar forms (1976)
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    Computing 16 (1976), S. 281-290 
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    Description / Table of Contents: Zusammenfassung Die Menge der Interpretationen einer (oder aller) kontext-freier Grammatikformen modulo starker Äquivalenz ist hinsichtlich der Ordnungsrelation „ist Interpretation von” ein distributiver Verband. Es wird ferner gezeigt, daß man für jede kontext-freie Grammatikform eine im wesentlichen eindeutige stark äquivalente kontext-freie Grammatikform konstruieren kann, die hinsichtlich der Anzahl der Produktionen minimal ist.
    Notes: Abstract It is shown that the set of all interpretations of one (or of all) context-free grammar forms modulo strong equivalence is a distributive lattice with respect to the ordering relation “is an interpretation of”. It is also established that for each context-free grammar form there exists a unique (up to “pseudo-isomorphism”) symbol-tight, strongly equivalent context-free grammar form which is minimal with respect to the number of productions.
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    An associated maximization problem for two-person nonzero-sum separable games (1976)
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    Mathematical programming 10 (1976), S. 124-133 
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    Notes: Abstract It has been shown that two-person zero-sum separable games are associated with a maximization problem involving the cones and dual cones of the generalized moments of the players' mixed strategy sets. In this note it is observed that those results extend almost immediately to two-person nonzero-sum separable games, but that then-person extension does not follow except in a special case.
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    Mathematical programming study 3 (1976)
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    Mathematical programming 10 (1976), S. 141-143 
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    Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems (1976)
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    Mathematical programming 10 (1976), S. 147-175 
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    Notes: Abstract For nonlinear programming problems which are factorable, a computable procedure for obtaining tight underestimating convex programs is presented. This is used to exclude from consideration regions where the global minimizer cannot exist.
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    Linear complementarity problems solvable by A single linear program (1976)
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    Mathematical programming 10 (1976), S. 263-270 
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    Notes: Abstract It is shown that the linear complementarity problem of finding az inR n such thatMz + q ⩾ 0, z ⩾ 0 andz T (Mz + q) = 0 can be solved by a single linear program in some important special cases including those whenM or its inverse is a Z-matrix, that is a real square matrix with nonpositive off-diagonal elements. As a consequence certain problems in mechanics, certain problems of finding the least element of a polyhedral set and certain quadratic programming problems, can each be solved by a single linear program.
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    Decomposing symmetric exchanges in matroid bases (1976)
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    Mathematical programming 10 (1976), S. 271-276 
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    Notes: Abstract LetB,B′ be bases of a matroid, withX ⊂ B, X′ ⊂ B′. SetsX,X′ are asymmetric exchange if(B − X′) ⋃ X′ and(B′ − X′) ⋃ X are bases. SetsX,X′ are astrong serial B-exchange if there is a bijectionf: X → X′, where for any ordering of the elements ofX, sayx i ,i = 1, ⋯, m, bases are formed by the sets B0 = B, Bi = (Bi−1 − xi) ⋃f(x i), fori = 1, ⋯, m. Any symmetric exchangeX,X′ can be decomposed by partitioning X = ⋃ i=1 m Yi, X′ = ⋃ i=1 m Yi, X′, where (1) bases are formed by the setsB 0 =B, B i = (B i−1 −Y i )⋃ Y i ′ ; (2) setsY i ,Y i ′ are a strong serialB i−1 -exchange; (3) properties analogous to (1) and (2) hold for baseB′ and setsY i ′ ,Y i .
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    Ray Fulkerson (1976)
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    Mathematical programming 10 (1976), S. 408-408 
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    Matrix factorizations in optimization of nonlinear functions subject to linear constraints (1976)
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    Mathematical programming 10 (1976), S. 1-31 
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    Notes: Abstract Several ways of implementing methods for solving nonlinear optimization problems involving linear inequality and equality constraints using numerically stable matrix factorizations are described. The methods considered all follow an active constraint set approach and include quadratic programming, variable metric, and modified Newton methods.
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    The factorization approach to large-scale linear programming (1976)
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    Mathematical programming 10 (1976), S. 91-110 
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    Notes: Abstract A unifying concept for large-scale linear programming is developed. This approach, calledfactorization, allows one to isolate the effect of different types of constraints and variables in the algebraic representation of the tableau. Two different factorizations based on a double representation of the tableau are developed. These factorizations are applied to obtain the essential structure of efficient algorithms for generalized upper bounding, coupled block-diagonal problems, set partitioning LPs, minimum cost network flows, and other classes of problems.
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    The Mathematical Programming Society (1976)
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    Mathematical programming 11 (1976), S. 103-103 
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    Maximization of A convex quadratic function under linear constraints (1976)
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    Mathematical programming 11 (1976), S. 117-127 
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    Notes: Abstract This paper addresses itself to the maximization of a convex quadratic function subject to linear constraints. We first prove the equivalence of this problem to the associated bilinear program. Next we apply the theory of bilinear programming developed in [9] to compute a local maximum and to generate a cutting plane which eliminates a region containing that local maximum. Then we develop an iterative procedure to improve a given cut by exploiting the symmetric structure of the bilinear program. This procedure either generates a point which is strictly better than the best local maximum found, or generates a cut which is deeper (usually much deeper) than Tui's cut. Finally the results of numerical experiments on small problems are reported.
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    Some theoretical implications of local optimization (1976)
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    Mathematical programming 10 (1976), S. 354-366 
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    Notes: Abstract This paper presents some theoretical results concerning the effectiveness of an approximate technique, known as local optimization, as applied to a wide class of problems. First, conditions are described under which the technique ensures exact solutions. Then, in regard to cases in which these conditions cannot be met in practice, a method is presented for estimating the probability that the approximate (locally optimal) solution delivered by such a technique is in fact the exact (globally optimal) solution. This probability may be viewed as a possible criterion of effectiveness in the design of neighborhoods for specific local optimization algorithms.
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    Some computationally relevant group theoretic structures of fixed charge problems (1976)
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    Mathematical programming 10 (1976), S. 379-400 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Among the most commonly occurring mixed-integer problems in operations research are linear programs with fixed charge objective functions. In this paper special structures of the equivalent form of such problems obtained from optimal solutions to their continuous relaxations are characterized and exploited in a series of penalty procedures for branch-and-bound type algorithms. The selection, construction, and solution of such penalty problems are discussed, and computational experience with the procedures is presented.
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    URL: http://dx.doi.org/10.1007/BF01580683
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    Editorial policy (1976)
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    Mathematical programming 10 (1976), S. 414-414 
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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/BF01580689
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    Global optimization using special ordered sets (1976)
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    Mathematical programming 10 (1976), S. 52-69 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The task of finding global optima to general classes of nonconvex optimization problem is attracting increasing attention. McCormick [4] points out that many such problems can conveniently be expressed in separable form, when they can be tackled by the special methods of Falk and Soland [2] or Soland [6], or by Special Ordered Sets. Special Ordered Sets, introduced by Beale and Tomlin [1], have lived up to their early promise of being useful for a wide range of practical problems. Forrest, Hirst and Tomlin [3] show how they have benefitted from the vast improvements in branch and bound integer programming capabilities over the last few years, as a result of being incorporated in a general mathematical programming system. Nevertheless, Special Ordered Sets in their original form require that any continuous functions arising in the problem be approximated by piecewise linear functions at the start of the analysis. The motivation for the new work described in this paper is the relaxation of this requirement by allowing automatic interpolation of additional relevant points in the course of the analysis. This is similar to an interpolation scheme as used in separable programming, but its incorporation in a branch and bound method for global optimization is not entirely straightforward. Two by-products of the work are of interest. One is an improved branching strategy for general special-ordered-set problems. The other is a method for finding a global minimum of a function of a scalar variable in a finite interval, assuming that one can calculate function values and first derivatives, and also bounds on the second derivatives within any subinterval. The paper describes these methods, their implementation in the UMPIRE system, and preliminary computational experience.
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    URL: http://dx.doi.org/10.1007/BF01580653
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    Win probabilities and simple majorities in probabilistic voting situations (1976)
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    Mathematical programming 11 (1976), S. 28-41 
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    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper considers an election between candidatesA andB in which (1) voters may be uncertain about which candidate they will vote for, and (2) the winner is to be determined by a lottery betweenA andB that is based on their vote totals. This lottery is required to treat voters equally, to treat candidates equally, and to respond nonnegatively to increased support for a candidate. The setΛ n of all such lottery rules based on a total ofn voters is the convex hull of aboutn/2 ‘basic’ lottery rules which include the simple majority rule. For odd values ofn ≥ 3 let $$\mu (n) = \tfrac{1}{2} + (n - 1)/[2n(n + 3)]$$ , and for even values ofn ≥ 4 let $$\mu (n) = \tfrac{1}{2} + [(n + 2)(2n(n + 2))^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} - n(n + 6)]/[n(n - 2)(n + 4)]$$ . With $$\bar p$$ the average of then voters probabilities of voting forA, it is shown that withinΛ n the simple majority rule maximizes candidateA's overall win probability whenever $$\bar p \geqslant \mu (n)$$ , and thatμ(n) is the smallest number for which this is true. Similarly, the simple majority rule maximizesB's overall win probability whenever $$1 - \bar p$$ (the average of the voters probabilities of voting forB) is as large asμ(n).
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    URL: http://dx.doi.org/10.1007/BF01580368
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    Another note on bimatrix games (1976)
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    Mathematical programming 11 (1976), S. 299-300 
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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/BF01580398
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    Surface roughness measurements from coherent light scattering (1976)
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    Optical and quantum electronics 8 (1976), S. 323-327 
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    ISSN: 1572-817X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract Results are presented of surface roughness measurements obtained by applying Beckmann's theory on the scattering of electromagnetic waves from rough surfaces to the scattering of laser light from ground glass surfaces. Measurements of the variance of surface height obtained in several scattering geometries and also from stylus measurements are presented and shown to agree closely for each surface. Also results are presented which show that the usual assumption of a Gaussian form for the autocorrelation function of surface height does not apply to the surfaces being studied here.
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    URL: http://dx.doi.org/10.1007/BF00619545
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    Effects of film nonlinearities on the signal-to-ghost ratio of storage holograms (1976)
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    Optical and quantum electronics 8 (1976), S. 355-365 
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    ISSN: 1572-817X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract A theory of film nonlinearities relating to amplitude holograms and bleached phase holograms is developed which is adapted to the problem of the holographic storage of digital data. The amplitude transmittance characteristics are for this purpose expanded in power series. The odd higher-order terms of the expansion yield expressions defining ghost spots that impair image quality.
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    URL: http://dx.doi.org/10.1007/BF00619549
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    A new characteristic of the neutron-irradiated silicon solar cells (1976)
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    Optical and quantum electronics 8 (1976), S. 367-370 
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    ISSN: 1572-817X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00619550
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    Operation of a narrow-band CW tuneable dye-laser at 656 nm (1976)
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    Optical and quantum electronics 8 (1976), S. 371-372 
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    ISSN: 1572-817X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00619551
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    Conference announcements 1976 (1976)
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    Optical and quantum electronics 8 (1976), S. 373-373 
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    ISSN: 1572-817X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00619552
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    Theory of the double heterostructure laser: II. Waveguide model incorporating carrier concentration-dependent refractive index (1976)
    Springer
    Optical and quantum electronics 8 (1976), S. 373-381 
    Details
    ISSN: 1572-817X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract Solutions to charge transport equations are used to illustrate the variation of the active region refractive index of the double-heterostructure GaAs laser. It is shown that a marked asymmetry can arise in the refractive index. In this paper, a suitable waveguide theory is developed to take account of this effect. The necessity for such a waveguide theory is demonstrated by comparing threshold current densities and far-field patterns calculated with this model to those calculated using a simpler waveguide model.
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    URL: http://dx.doi.org/10.1007/BF00624828
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    The self-action of the electromagnetic field in a medium with considerable nonlinearity (1976)
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    Optical and quantum electronics 8 (1976), S. 393-398 
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    ISSN: 1572-817X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract The propagation of the electromagnetic wave field in a nonlinear medium is discussed in the framework of generalized nonlinear geometrical optics. In this approach the nonlinearity of the medium and the angles between the rays and the general orientation of the wave's beam are not assumed to be small. The exact analytical solutions of the equations of this generalized nonlinear geometrical optics are constructed. These solutions show the possibility of a peculiar mechanism of space stratification of the field.
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    URL: http://dx.doi.org/10.1007/BF00624830
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    Theory of the double heterostructure laser: III. Self-consistent calculations of the electrical and optical characteristics (1976)
    Springer
    Optical and quantum electronics 8 (1976), S. 383-391 
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    ISSN: 1572-817X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract Self-consistent calculations of the electrical and optical properties of the double-heterostructure laser have been made. Theoretical studies of both aspects of the device performance have been utilized in this work which describes the behaviour of the laser both below and at threshold. The interdependence of the electrical and optical properties of the device has been established and incorporated into a self-consistency scheme. A computer program has been developed to perform the calculations given the specification of device parameters. Within the program the transport equations are solved, the active region refractive index calculated and then used in the waveguide theory. From the solution to the waveguide equations a lasing frequency and threshold current for the specified cavity mode are obtained. A consistency criterion is applied between the transport and waveguide parts of the theory. The program allows the performance of the laser to be monitored providing such information asI–V characteristics, near and far field patterns for various cavity modes with their threshold currents and lasing frequencies.
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    URL: http://dx.doi.org/10.1007/BF00624829
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    A large coaxial lidar for elastic and inelastic scattering studies of the stratosphere (1976)
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    Optical and quantum electronics 8 (1976), S. 409-423 
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    ISSN: 1572-817X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract A very powerful, fixed zenith laser radar system, based upon a liquid dye laser, is described in detail. The laser is a linear flashlamp pumped dye system capable of an average power output of 6W at a prf of 3 s−1 using rhodamine 6G dye and about 3W with the same prf using esculin monohydrate dye. The use of this laser as a transmitting source in the lidar system has permitted the detection of Stokes shifted vibration/rotation Raman back-scattered light from neutral nitrogen in the stratosphere and from these measurements, stratospheric temperature profiles have been derived. The lidar has also been used to study elastic backscattering from the stratosphere at two wavelengths and preliminary results of a new technique for studying stratospheric aerosol are presented.
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    URL: http://dx.doi.org/10.1007/BF00624832
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