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  • 101
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    Bulletin of mathematical biology 44 (1982), S. 609-635 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper deals with the unimodality of the ‘impulse response’ in compartmental systems, where the ‘impulse response’ in any given compartment is the time course of the amount of diffusing substance in that compartment after an initial instantaneous injection of the substance into that or some other compartment. It is shown that in certain compartmental structures, with injection in certain compartments, the impulse response is always unimodal or monotonic in all compartments, regardless of the numerical values of the various transfer rate coefficients. Structures with this property are here named ‘UM structures’, and they include the familiar mammillary and catenary structures. In this paper, the set of all UM structures is described. Structures which are not UM (NUM structures) are identified by showing that, by removal of certain connections and compartments according to certain rules, they can be reduced to small structures which can be shown to be NUM by numerical computation. Computations on two systems with bimodal impulse responses show that with constant infusions of a fixed amount of substance the peak level may increase paradoxically with decrease in the infusion rate over a certain range. This effect is extremely small, however.
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  • 102
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    Bulletin of mathematical biology 44 (1982), S. 661-668 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Arbib in a paper entitled ‘Categories of (M, R)-Systems' represents both simple (M, R)-systems and those with varying genome as subcategories of the category of automata. An alternative characterisation of general (M, R)-systems as automata is proposed and two theorems on (M, R)-automata are proved. The two categories of automata, namely Arbib in a paper entilled ‘Categories of (M,R)-Systems’ represents both simple (M, R)-systems with variable genetic structure, are compared.
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  • 103
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    Bulletin of mathematical biology 44 (1982), S. 647-659 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Developed in this paper is an eight-parameter model of human mortality. A step-wise nonlinear least-squares procedure for estimating the parameters from abridged life tables is also described and implemented. Used for purposes of illustration were nine period life tables, ranging from 1900 to 1977, for the United States white male population. The agreement between the observed and calculated survival functions in the nine life tables was very good. Apart from its phenomenological interest, the model provides an effective means for calculating interpolations and extrapolations of abridged life tables, which are useful making population projections and in computer graphics.
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  • 104
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    Bulletin of mathematical biology 44 (1982), S. 669-687 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract The determinationof electric potentials in finite regions of symmetrical electrolyte in one-dimensional equilibrium situations requires the solution of the one-dimensional Poisson-Boltzmann equation in which the dependent variable is linearly related to the electric potential and contains unknown parameters. These require evaluation as part of the solution to a given boundary value problem. The general solution of the equation is presented. This involves elliptic functions and integrals and is sectionally isomorphic with respect to an integration parameter. The application to problems posed in terms of both initial values and two-point boundary values is discussed. The solution is used to determine the potential and concentration distributions between two flat-faced charged particles immersed in an electrolyte liquid and having interacting double layers.
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  • 105
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    Bulletin of mathematical biology 44 (1982), S. 689-696 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A brief review of measurement theory in quantum mechanical and biological systems is made, the concept of quantum nondemolition experiments is discussed and a possible resolution to a previous discussion on the existence of nonrepeatable experiments is presented.
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  • 106
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    Bulletin of mathematical biology 44 (1982), S. 697-704 
    ISSN: 1522-9602
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    Topics: Biology , Mathematics
    Notes: Abstract This paper has studied the evolution of a predator-prey Volterra-Lotka ecosystem with saturation effect for the general case where both predator and prey evolve. We have interesting results under the evolutional condition, as follows: (1) the predator population and the ratio of predator to prey populations increase; (2) the parameters of the prey drift in the direction of increasing multiplication rate and saturation level, while the parameters of the predator drift in the direction of decreasing death rate.
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  • 107
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    Mathematical programming 22 (1982), S. 71-81 
    ISSN: 1436-4646
    Keywords: Blocking ; Antiblocking ; Polarity ; Penumbra
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract E. Johnson has recently shown that the concept of a penumbra leads to a simple geometric description of the blocker and antiblocker of a given set. Here we develop some basic results on penumbras which permit us to slightly generalize and simplify results on their relationship to blocking and antiblocking theory. In addition, motivated by the obvious symmetry of our results, we examine the effect of reversing the blocking and antiblocking operations.
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  • 108
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    Mathematical programming 22 (1982), S. 121-121 
    ISSN: 1436-4646
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    Topics: Computer Science , Mathematics
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  • 109
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    Mathematical programming 22 (1982), S. 148-162 
    ISSN: 1436-4646
    Keywords: Set Covering Problem ; Median Problem ; Location Problems ; Heuristics ; Worst Case Analysis ; Continuous Location Problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We describe in this paper polynomial heuristics for three important hard problems—the discrete fixed cost median problem (the plant location problem), the continuous fixed cost median problem in a Euclidean space, and the network fixed cost median problem with convex costs. The heuristics for all the three problems guarantee error ratios no worse than the logarithm of the number of customer points. The derivation of the heuristics is based on the presentation of all types of median problems discussed as a set covering problem.
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  • 110
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    Mathematical programming 22 (1982), S. 227-230 
    ISSN: 1436-4646
    Keywords: Minimax ; Nonconvex Optimization ; Stationary Points
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We give a short proof that in a convex minimax optimization problem ink dimensions there exist a subset ofk + 1 functions such that a solution to the minimax problem with thosek + 1 functions is a solution to the minimax problem with all functions. We show that convexity is necessary, and prove a similar theorem for stationary points when the functions are not necessarily convex but the gradient exists for each function.
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  • 111
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    Mathematical programming 24 (1982), S. 257-268 
    ISSN: 1436-4646
    Keywords: Nondifferentiable Programming ; Convex Analysis ; Sensivity Analysis ; Duality Theory ; Second Order Derivative ; Second Order Methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We study differential properties of the support function of the∈-subdifferential of a convex function; applications in algorithmics are also given.
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  • 112
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    Mathematical programming 22 (1982), S. 93-103 
    ISSN: 1436-4646
    Keywords: Linear Programming ; Relaxation Method ; Polynomiality
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    Topics: Computer Science , Mathematics
    Notes: Abstract A class of linear programs is given in which the relaxation method for inequalities, under the same operating rules as Khacian's method, is not polynomial in the length of the input. This result holds for any value of the relaxation parameter.
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  • 113
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    Mathematical programming 22 (1982), S. 117-120 
    ISSN: 1436-4646
    Keywords: Augmenting Path Algorithm ; Boolean Lattice ; Jordan-Hölder Theorem ; Matroid Intersection
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract It is noted that the decomposition of a network presented by J.C. Picard and M. Queyranne through an algorithmic argument may be defined from a general lattice-theoretic result for more general problems for which the equalities of maximum-flow minimum-cut type hold.
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  • 114
    ISSN: 1436-4646
    Keywords: Geometric Programming ; Code Comparisons ; Numerical Testing ; Nonlinear Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Ten codes or code variants were used to solve the five equivalent posynomial GP problem formulations. Four of these codes were general NLP codes; six were specialized GP codes. A total of forty-two test problems was solved with up to twenty randomly generated starting points per problem. The convex primal formulation is shown to be intrinsically easiest to solve. The general purpose GRG code called OPT appears to be the most efficient code for GP problem solution. The reputed superiority of the specialized GP codes GGP and GPKTC appears to be largely due to the fact that these codes solve the convex primal formulation. The dual approaches are only likely to be competitive for small degree of difficulty, tightly constrained problems.
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  • 115
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    Mathematical programming 22 (1982), S. 231-235 
    ISSN: 1436-4646
    Keywords: Integer Programming ; Covering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract LetA be a non-negative matrix with integer entries and no zero column. The integer round-up property holds forA if for every integral vectorw the optimum objective value of the generalized covering problem min{1y: yA ≥ w, y ≥ 0 integer} is obtained by rounding up to the nearest integer the optimum objective value of the corresponding linear program. A polynomial time algorithm is presented that does the following: given any generalized covering problem with constraint matrixA and right hand side vectorw, the algorithm either finds an optimum solution vector for the covering problem or else it reveals that matrixA does not have the integer round-up property.
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  • 116
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    Mathematical programming 22 (1982), S. 12-38 
    ISSN: 1436-4646
    Keywords: Graph ; Matching ; Branching ; Linear Programming ; Polyhedron
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Matching forests generalize branchings in a directed graph and matchings in an undirected graph. We present an efficient algorithm, the PMF Algorithm, for the problem: given a mixed graphG and a real weight on each of its edges, find a perfect matching forest of maximum weight-sum. The PMF Algorithm proves the sufficiency of a linear system which definesP = (G) andP(G), the convex hull of incidence vectors of perfect matching forests and matching forests respectively ofG. The algorithm also provides a generalization of Tutte's theorem on the existence of perfect matchings in an undirected graph.
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  • 117
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    Mathematical programming 22 (1982), S. 122-123 
    ISSN: 1436-4646
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  • 118
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    Mathematical programming 22 (1982), S. 141-147 
    ISSN: 1436-4646
    Keywords: Integer Rounding ; Pluperfect Graphs ; Combinatorial Optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract LetA be a nonnegative integral matrix with no zero columns. Theinteger round-up property holds forA if for each nonnegative integral vectorw, the solution value to the integer programming problem min{1 ⋅y: yA ≥ w, y ≥ 0, y integer} is obtained by rounding up to the nearest integer the solution value to the corresponding linear programming problem min{1 ⋅y: yA ≥ w, y ≥ 0}. Theinteger round-down property is similarly defined for a nonnegative integral matrixB with no zero rows by considering max{1 ⋅y: yB ≤ w, y ≥ 0, y integer} and its linear programming correspondent. It is shown that the integer round-up and round-down properties can be checked through a finite process. The method of proof motivates a new and elementary proof of Fulkerson's Pluperfect Graph Theorem.
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  • 119
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    Mathematical programming 22 (1982), S. 236-237 
    ISSN: 1436-4646
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    Topics: Computer Science , Mathematics
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  • 120
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    Mathematical programming 22 (1982), S. 304-315 
    ISSN: 1436-4646
    Keywords: Location Theory ; Tree Networks ; Rigid Circuit Graphs ; Polynomial Algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We discuss several forms of thep-center location problems on an undirected tree network. Our approach is based on utilizing results for rigid circuit graphs to obtain polynomial algorithms for solving the model. Duality theory on perfect graphs is used to define and solve the dual location model.
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  • 121
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    Mathematical programming 23 (1982), S. 111-116 
    ISSN: 1436-4646
    Keywords: Multicriteria Optimization ; Convex Analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Existence and characterization theorems for the efficient (nondominated) set of decisions inR n are presented. The existence is proved when the set of decisions satisfies some compactness conditions. The efficient set is characterized in terms of the exposed efficient decisions when certain convexity and compactness conditions are satisfied.
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  • 122
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    Mathematical programming 23 (1982), S. 170-180 
    ISSN: 1436-4646
    Keywords: Set Covering ; Heuristic Algorithms ; Worst Case Analysis ; Bounds
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In [2], Chvatal provided the tight worst case bound of the set covering greedy heuristic. We considered a general class of greedy type set covering heuristics. Their worst case bounds are dominated by that of the greedy heuristic.
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  • 123
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    Mathematical programming 23 (1982), S. 216-226 
    ISSN: 1436-4646
    Keywords: Nonsmooth Optimization ; Subgradient ; Subdifferential ; Bundle Type Method ; Deletion Rule ; Resetting
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A numerical method for the unconstrained minimization of a convex nonsmooth function of several variables is presented. It is closely related to the ‘bundle type’ approach and to the conjugate subgradient method. A way is suggested to reduce the amount of information to be stored during the computational procedure. Global convergence of the method to the minimum is proved.
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  • 124
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    Mathematical programming 23 (1982), S. 326-340 
    ISSN: 1436-4646
    Keywords: Optimization ; Quasi-Newton ; Conjugate Gradient
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    Notes: Abstract In this paper we study conjugate gradient algorithms for large optimization problems. These methods accelerate (or precondition) the conjugate gradient method by means of quasi-Newton matrices, and are designed to utilize a variable amount of storage, depending on how much information is retained in the quasi-Newton matrices. We are concerned with the behaviour of such methods on the underlying quadratic model, and in particular, with finite termination properties.
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  • 125
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    Mathematical programming 23 (1982), S. 357-360 
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  • 126
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    Monatshefte für Mathematik 93 (1982), S. 117-126 
    ISSN: 1436-5081
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    Topics: Mathematics
    Notes: Abstract The isometries with respect to the Hausdorff metric of spaces of compact or compact convex subsets of certain compact metric spaces are precisely the mappings generated by isometries of the underlying spaces. In particular this holds when the underlying space is a finite dimensional torus or a sphere in a finite dimensional strictly convex smooth normed space.
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  • 127
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    Monatshefte für Mathematik 93 (1982), S. 303-308 
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    Topics: Mathematics
    Notes: Abstract If a group acts on a finite projective plane to make it a plane of type (5,m) then the related 2-transitive permutation representation of it has a normal regular subgroup.
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  • 128
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    Monatshefte für Mathematik 93 (1982), S. 329-348 
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    Topics: Mathematics
    Notes: Abstract It is shown that a system ofr homogeneous cubic equations with rational coefficients has a nontrivial solution in rational integers if the number of variables is at least (10r)5. For most such systems, an asymptotic formula holds for the numberz P of solutions whose components have modulus 〈P.
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    Monatshefte für Mathematik 94 (1982), S. 33-44 
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    Topics: Mathematics
    Notes: Abstract The distribution of integers and prime numbers in sequences of the formF c1∩F c2 is investigated. HereF c={[n c]:n∈ ℕ} withc〉1.
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    Monatshefte für Mathematik 94 (1982), S. 103-107 
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    Topics: Mathematics
    Notes: Abstract Intervals in which Lagrange interpolation polynomials converge pointwise to the interpolated function are specified for a family of functions comprising all completely monotone functions.
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    Monatshefte für Mathematik 93 (1982), S. 39-62 
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    Notes: Abstract For a complex continued fraction algorithm the invariant measure for the shift transformation is determined explicitly in terms of elementary functions, and the transformation is shown to be ergodic. Analogues of well-known theorems of Khintchine and Lévy are obtained.
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    Monatshefte für Mathematik 93 (1982), S. 33-37 
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    Notes: Abstract A characterisation of all real Δ≠0 is given, such that $$\overline {f(\sigma + i\Delta \mathbb{N})} = \overline {f(\sigma + i\mathbb{R})} $$ holds for all Dirichlet seriesf(s)=Σa n n −s and all σ greater than the abscissa of absolute convergence off. For only countably many Δ relation (*) is not valid. By using transcendental results it is shown, that (*) holds in the special case, Δ=1.
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    Monatshefte für Mathematik 93 (1982), S. 75-78 
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    Monatshefte für Mathematik 93 (1982), S. 63-74 
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    Notes: Abstract Hua andChen gave estimates of sums $$\sum\limits_{x = 1}^q {e(\mathfrak{F}(x))} $$ wheree(z)=e 2πiz and $$\mathfrak{F}$$ is a polynomial of the typef(x)/q wheref(x)=a k x k +...+a 1 x with integer coefficients having gcd (q, a k ,...,a 1)=1 But no good estimates hold for these sums whenq is small in comparison tok. We therefore consider here a related but different class of polynomials. Special emphasis is given to the cubic case. In subsequent papers of this series we shall deal with cubic exponential sums in many variables and withp-adic and rational zeros of systems of cubic forms.
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    Monatshefte für Mathematik 93 (1982), S. 79-110 
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    Notes: Abstract The specification property for solenoidal automorphisms is discussed; a solenoidal automorphism σ satisfies specification iff σ is expansive, and σ satisfies weak specification but not specification iff σ is ergodic and central spin. These are problems set up byK. Sigmund for homeomorphisms with specification. The proofs for toral case are given byD. Lind. For solenoidal case, a key ingredient in our proofs is splitting theorems on solenoidal groups with respect to σ described in § 2. Moreover, the following is proved: (i) If σ obeys specification then σ satisfies weak specification and is densely periodic. But the converse is not necessarily true. (ii) Every solenoidal automorphism with specification admits a Markov partition. (iii) Every ergodic solenoidal automorphism without specification does not admit Markov partitions. (iv) There exists an expansive homeomorphism with specification which has not Markov partitions.
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    Monatshefte für Mathematik 93 (1982), S. 169-172 
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    Monatshefte für Mathematik 93 (1982), S. 261-265 
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    Notes: Abstract FollowingKazhdan, a separable locally compact groupG is said to have propertyT if the trivial representation is isolated in the dual space,Ĝ, of equivalence classes of continuous irreducible unitary representations ofG. We generalize results ofMargulis—Tits by showing that groups which have propertyT can not be amalgams.
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    Monatshefte für Mathematik 93 (1982), S. 267-275 
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    Notes: Abstract On the Interpolation of Maximal Monotone Operators. We study here one way to extend to the maximal monotone case the results of linear interpolation, exposed bybalakrishnan in [2]. We obtain a necessary and sufficient condition of convergence for sequences(A n ) n of maximal monotone operators on a real Hilbert spaceH.
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    Monatshefte für Mathematik 94 (1982), S. 249-261 
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    Topics: Mathematics
    Notes: Abstract The notion of dispersion, a measure of denseness of sequences, plays an important role in quasi-Monte Carlo optimization. In this paper, we obtain an explicit formula for the dispersion of an important low dispersion sequence, namely the Hammersley Sequence in the unit square. The dispersiond M of theM points of this sequence, whereM=2N withN a positive integer is given by $$d_M = \frac{{\sqrt {2M - 2\sqrt M + 1} }}{M},if N is even, d_M = \frac{{\sqrt {\left( {5/2} \right)M - \sqrt {8M} + 1} }}{M},if N is odd.$$ .
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    Monatshefte für Mathematik 94 (1982), S. 213-248 
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    Notes: Abstract Let the continuous broken linear transformationf of the unit interval into itself satisfyingf(0)=f(1)=0 be determined by the coordinates of its peak pointP (x, y). The topological entropyh off, as a function of (x, y), is zero outside the triangle max (x, 1−x)〈y≤1. Inside it is shown to be nonzero, continuous, monotonically increasing both iny/x and iny/(1−x) and to assume its maximum log2 ony=1. The level curvec(h 0) of constant corresponding entropyh 0〉0 is a continuous curve joining the two diagonalsy=x andy=1−x in whichh has discontinuities (jumping to zero). For 1/2log2〈h≤log 2 the curvesc(h) pass through (0,1) withy=1 as a tangent and fill up the area bounded below by the parabolay 2=1−x on whichh(x,y)=1/2 log 2. For 1/2 log 2 〈h ⩽ log 2 the curvec(h) is the image of the arc ofc(2h) between the hyperbolax 2−xy2x+1=0 and the diagonaly=1−x under the transformation $$T\left( {x,y} \right) = \left( {1 - x,\sqrt {xy} } \right)$$ .
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    Monatshefte für Mathematik 94 (1982), S. 335-341 
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    Topics: Mathematics
    Notes: Abstract A criterion for a measure preserving transformation to be “prime” is given. The criterion allows the transformation to have uncountable centralizer.
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    Monatshefte für Mathematik 94 (1982), S. 313-333 
    ISSN: 1436-5081
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    Topics: Mathematics
    Notes: Abstract For a certain class of piecewise monotonic transformations it is shown using a spectral decomposition of the Perron-Frobenius-operator ofT that invariant measures depend continuously on 3 types of perturbations: 1) deterministic perturbations, 2) stochastic perturbations, 3) randomly occuring deterministic perturbations. The topology on the space of perturbed transformations is derived from a metric on the space of Perron-Frobenius-operators.
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    OR spectrum 3 (1982), S. 193-198 
    ISSN: 1436-6304
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    Topics: Mathematics , Economics
    Description / Table of Contents: Summary Using a concrete example two linear optimization models based on the following cutting stock problem are compared: A stock of rolls of a synthetic cloth has to be cut such that the sum of net returns and the value of the residual stock at the end of the planning period is maximized. Since a limited number of cutting patterns is heuristically choosen the first model yields sub-optimal solutions only. On the contrary, the second model usesall relevant cutting patterns and provides an optimal solution.
    Notes: Zusammenfassung An einem realen Beispiel werden zwei lineare Optimierungsmodelle verglichen, denen folgendes Dispositionsproblem zugrunde liegt: Ein Ausgangsprodukt ist durch Verschnitte so weiter zu verarbeiten, daß die Summe aus Nettoerlösen und bewerteten Restbeständen auf Lager maximal wird. Das erste Modell liefert aufgrund einer beschränkten Anzahl heuristisch vorgegebener Schnittmuster i. a. nur suboptimale Lösungen. Das zweite, verbesserte Modell berücksichtigt im Gegensatz dazualle sinnvollen Schnittmuster und führt zu einer optimalen Lösung.
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    OR spectrum 3 (1982), S. 225-231 
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    Description / Table of Contents: Zusammenfassung In diesem Artikel werden Flußprobleme in Netzwerken betrachtet, in denen jedem Pfeil neben der Kapazität auch fixe Kosten zugeordnet werden. Diese Kosten fallen an, sobald ein Fluß größer Null durch den Pfeil fließt. Zielsetzung ist die Maximierung des Netzflusses unter der Bedingung, daß ein gegebenes Budget nicht überschritten wird. Einige Anwendungen dieses Problems werden aufgezeigt und eine Strukturanalyse wird durchgeführt, anschließend wird ein Approximationsalgorithmus entwickelt. In einer kleinen Testreihe werden die Lösungen dieses Algorithmus' mit den exakten Lösungen verglichen.
    Notes: Summary Network flow problems are considered in which in addition to the capacities fixed costs are assigned to each arc which are incurred as soon as any positive flow is sent through that arc. It is the objective to maximize the flow so that the fixed costs do not exceed a given budget. Some applications of this problem are described and a structural analysis is performed. In addition to that an approximation algorithm is developed and its results are compared to the exact solutions in a small test series.
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    OR spectrum 3 (1982), S. 245-245 
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    Description / Table of Contents: Summary Efficiency considerations in the field of health become more and more urgent. This paper deals with the problem of determining the optimal size, organizational form and input structure of a general practice in dependence on the number of patients to be provided for. As solution approach a linear output oriented production model with the possibilities of choosing different production processes will be discussed. Subsequently the methodical considerations will be applied to a consulting practice of ophthalmology, and the results are exposed.
    Notes: Zusammenfassung Wirtschaftlichkeitsüberlegungen im Gesundheitssektor werden immer dringlicher. Der vorliegende Beitrag befaßt sich mit dem Problem der optimalen Betriebsgröße, Organisationsform und Inputstruktur einer Arztpraxis in Abhängigkeit der Größe des zu versorgenden Patientenstammes. Als Lösungsansatz wird ein lineares output-orientiertes Produktionsmodell mit verschiedenen Verfahrenswahlmöglichkeiten diskutiert. Die methodischen Überlegungen werden anschließend auf eine Facharztpraxis für Augenheilkunde angewendet und die Ergebnisse dargelegt.
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    OR spectrum 4 (1982), S. 52-52 
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    OR spectrum 4 (1982), S. 47-51 
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    Description / Table of Contents: Zusammenfassung Für das WartemodellE k /D/r wird über die „steady state Gleichungen“ die erzeugende Funktion der Verteilung der Warte Schlangenlänge hergeleitet. Die mittlere Zahl der Einheiten im System und verwandte Größen werden in geschlossener Form mit Hilfe der Wurzeln einer transzendenten Gleichung dargestellt. Diese Wurzeln können leicht mit numerischen Standard-verfahren bestimmt werden. Ein Algorithmus zur Bestimmung der stationären Verteilung der Zahl der Einheiten im System wird entwickelt. Numerische Ergebnisse für die mittleren Wartezeiten werden fürk=2,r=1, 2, ..., 10, und variable Verkehrsintensität angegeben.
    Notes: Summary In this paper we study theE k /D/r queueing system. The steady state equations are derived and the queue lenth probability generating function is determined. The average number of customers in the system and other related quantities are determined in closed form in terms of the roots of an equation, which can be easily obtained by standard numerical techniques. Also a computational procedure for evaluating the steady state probability distribution of the number of customers in the system is developed. Numerical results of the average queueing times are given fork=2,r=1, 2, ..., 10 and the whole range of utilization factors.
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    OR spectrum 4 (1982), S. 79-89 
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    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Wir betrachten ein periodisch kontrolliertes dynamisches Mehrprodukt-Lagerhaltungsmodell mit stochastischem Bedarf, bei dem sich die Bestellkosten aus einem linearen und einem nichtlinearen Anteil zusammensetzen. Der nichtlineare Anteil kann z. B. davon abhängen, welche Produkte bestellt werden. Es wird die Existenz einer optimalen Bestellpolitik gezeigt. Außerdem werden Eigenschaften einer solchen Politik nachgewiesen. Wir zeigen, daß bei Spezialisierung der nichtlinearen Bestellkosten eine optimale Politik eine (σ, S)-Politik ist. Die Ergebnisse beziehen sich auf den endlichen Planungshorizont.
    Notes: Summary We consider a period review, dynamic multiproduct inventory model with stochastic demand, in which the cost of ordering consists of linear portions for each product as well as a nonlinear term. This nonlinear term depends for example, on the products we order. We prove the existence of an optimal policy and characterize such a policy. We show that an optimal policy reduces to the well-known (σ, S)-policy, if we spezialise the nonlinear ordering cost in a proper way. Finite horizon results are given.
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    OR spectrum 4 (1982), S. 105-112 
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    Topics: Mathematics , Economics
    Description / Table of Contents: Summary The paper has two purposes. First, it is shown that for many cases of practical interest the optimal selection of the depreciation method can be made independently from the selection of the financing-mix. Second, a mixed-integer linear programming for a simplified dynamic version of the problem is developed for the determination of the optimal financing-mix and — if necessary — the simultaneous selection of the depreciation method.
    Notes: Zusammenfassung Dieser Artikel verfolgt zwei Absichten: zum einen wird gezeigt, daß in bestimmten Fällen die Wahl der optimalen Abschreibungsmethode für Ein- und Zweifamilienhäuser unabhängig von der Festlegung des Finanzierungsmixes erfolgen kann, zum zweiten wird ein dynamisches gemischt-ganzzahliges lineares Programm vorgestellt, welches den Finanzierungsmix optimiert unter gleichzeitiger Festlegung der Abschreibungsmethode.
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    OR spectrum 4 (1982), S. 129-134 
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    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Minimale Kostenflußprobleme mit nichtlinearen parametrischen Bewertungsfunktionenc(t) T x mitt aus dem Intervall [t min,t max] werden untersucht. Es wird eine endliche Folge zuläs siger Basen (B k ¦k =1, 2,...,r) bestimmt, die inI k := [t k , tk+1] optimal sind (k=1, 2, ...,r;t min=t 1 〈t 2 〈 ... 〈t r+1=t max). Die Teilintervalle Ik werden durch die Berechnung von Nullstellen bestimmter nichtlinearer Funktionen ermittelt. Numerische Ergebnisse werden für den Spezialfall polynomialer parametrischer Kostenfunktionen diskutiert.
    Notes: Summary Minimal cost network flow problems with nonlinear parametric objective functionsc(t) T x fortε[t min,t max] are studied. A finite sequence of feasible bases (B k ¦k =1, 2, ...,r) optimal in [t k , tk+1] fork=1, 2,...,r witht min=t 1〈t 2〈...〈t r+1=t max is determined using the zeroes of a set of nonlinear functions. Computional experience is discussed in the special case of polynomial parametric objective functions.
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    OR spectrum 3 (1982), S. 205-219 
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    Topics: Mathematics , Economics
    Description / Table of Contents: Summary In this article a mode of inventory taking is presented, which connects the system of perpetual inventory taking with sampling methods. Details of this mode are analyzed and a precise and economic procedure is developed. For special mathematical problems occurring with modifications of the sample solutions are presented.
    Notes: Zusammenfassung Es wird eine Inventurform behandelt, die das System der permanenten Inventur mit dem Verfahren der stichprobenartigen Erfassung verbindet. Details dieser Inventurform werden analysiert und ein korrektes und wirtschaftliches Vorgehen wird entwickelt. Für spezielle bei einer Stichprobenmodifikation auftretende mathematische Probleme werden Lösungen vorgestellt.
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    OR spectrum 3 (1982), S. 244-244 
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    OR spectrum 3 (1982), S. 233-237 
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    Topics: Mathematics , Economics
    Description / Table of Contents: Summary Subject of this paper is the determination of a distance function defined on the set of observed characteristics of objects (individuals, goods, enterprises etc.). In contrast to the usual approach, where a dissimilarity coefficient exhibiting some more or less desirable properties is chosen, at first conditions to be met by the dissimilarity coefficient are set. Then the class of dissimilarity coefficients that meets these conditions is determined. It is shown, that four such conditions imply the weighted Lr-metric.
    Notes: Zusammenfassung Gegenstand dieses Beitrages ist die Ermittlung von Distanzindizes, die als Maß für die Ähnlichkeit von durch quantitative Merkmalsausprägungen charakterisierbaren Objekten verwandt werden können. Im Gegensatz zu dem üblichen Vorgehen, bei dem ein Distanzindex gewählt wird, der mehr oder weniger wünschenswerte Eigenschaften besitzt, werden zunächst Bedingungen formuliert, die als sinnvoll für den gesuchten Distanzindex angesehen werden. Anschließend wird die Klasse derjenigen Distanzindizes ermittelt, die diesen Bedingungen genügt. Es wird gezeigt, daß die Forderung von vier derartigen Bedingungen die gewichtete Lr-Distanz impliziert.
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    OR spectrum 3 (1982), S. 246-246 
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    OR spectrum 4 (1982), S. 1-14 
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    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Dieses Manuskript gibt einen Über-blick über den Stand der Forschung zur Anwendung der Kontrolltheorie bei der Analyse der Unternehmens-dynamik. Drei Modellarten werden betrachtet: ein Unternehmen in einer gewissen Umwelt, ein Unternehmen in einer stochastischen Umwelt mit der Möglichkeit des Bankrotts und Modelle, bei denen das Unternehmen in Konkurrenz zu einem anderen steht. Trotz der Grenzen dieser kontrolltheoretischen Modelle sind sie nützlich bei der Verbesserung des Verständnisses von bedeutenden mikroökonomischen Phänomena und wenn man Studenten oder Jungmanagern erklären will, wie man Politiken im Verlauf der Zeit kombiniert um eine wirksame Strategie zu entwickeln.
    Notes: Summary This paper gives an overview to the state-of-art of applying control theory to the analysis of the dynamics of the firm. Three types of models are considered: one firm facing a certain environment, one firm facing a stochastic environment and with a risk of bankruptcy, and models of duopolies. In spite of the limits of these control theory models, they are useful to improve the understanding of important microeconomic phenomena and to explain to students or to junior managers how to combine policies through time to define an efficient strategy. An extended bibliography is given.
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    OR spectrum 4 (1982), S. 27-33 
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    Topics: Mathematics , Economics
    Description / Table of Contents: Summary The author's thesis is that strategic decisions are usually madeoutside the formal strategic planning process, and that the latter largely consolidates at the corporate level the strategic decisions already made at lower levels. Hence there is little scope for quantitative decision models in this process, but considerable scope at the actual strategic decision making level. However, if the corporate process is changed to go beyond consolidation so that explicit choices from alternate corporate strategies are considered, an important new potential for quantitative modelling is opened up.
    Notes: Zusammenfassung Quantitative Modellierung möchte zur Entscheidungsfindung beitragen. Bevor untersucht wird, ob sie dies im strategischen Bereich tut, wird die Frage gestellt, ob die tatsächlichen strategischen Entscheidungen, die die Zukunft einer Unternehmung gestalten, innerhalb des formalen Prozesses der strategischen Unternehmensplanung fallen. Die Frage wird überwiegend verneint. Solange die Dinge so stehen, ist es nicht verwunderlich, daß quantitative Entscheidungsmodelle nichts beitragen können. Dagegen ist die modellgestützte Planung dort kräftig im Vordringen und hat in den letzten Jahren erheblich an Terrain gewonnen, wo derzeit die meisten strategischen Optionen getroffen werden, nämlich bei den fallweisen strategischen Entscheidungen in Teilbereichen, die später in den strategischen Plan der Unternehmung integriert werden. Doch finden sich auch erste fruchtbare Ansätze innerhalb der formalen strategischen Planung auf Unternehmensebene, nämlich dort, wo diese sich explizit mit Alternativstrategien beschäftigt. In dem Maße, in dem sich der formale Prozeß der strategischen Unternehmensplanung zu einem Entscheidungs-prozeß zwischen explizit zur Wahl gestellten Unternehmensstrategien entwickelt — eine Entwicklung, die bereits begonnen hat — wird sich der modellgestützten Planung auch auf der Unternehmensebene ein weites Feld eröffnen.
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    OR spectrum 4 (1982), S. 53-54 
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    OR spectrum 4 (1982), S. 63-77 
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    Description / Table of Contents: Summary The paper gives a survey of stock holding models being employed in practice. In particular it stresses the whole process which leads to a selection of a special model. Main attention is given to a discussion of the value of cost parameters and safety stocks.
    Notes: Zusammenfassung Die Arbeit gibt einen Überblick über die in der Praxis verwandten Lagerhaltungsmodelle und arbeitet besonders den gesamten Prozeß heraus, der zum Einsatz eines bestimmten Modells führt. Besonderer Wert wird dabei auf die Diskussion der zu verwendenden Kostenparameter und Sicherheitsbestände gelegt.
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    OR spectrum 4 (1982), S. 91-104 
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    Description / Table of Contents: Summary In this paper a 0/1 linear programming model is proposed to solve the following problem: Given a certain budget, which diagnostic strategies should be applied to which groups of a population in order to maximize the effectiveness of early detection of hypertension. The ideas underlying the LP-model originated in the critique of a method described in the literature. A simplified example of the model is solved and some remarks are made concerning data collection and computing time requirements. Also the problem of individual vs. collective effectiveness is briefly dealt with.
    Notes: Zusammenfassung Die vorliegende Arbeit entwickelt ein auf der linearen 0/1 Programmierung basierendes Verfahren zur gruppenspezifischen Auswahl von Diagnosestrategien bei beschränkten Ressourcen im Bereich der Hypertoniefrüherkennung. Ausgangspunkt ist dabei die Kritik an einer in der Literatur zu diesem Thema angegebenen Methode. Ein vereinfachtes Beispiel verdeutlicht die Ideen, die zur Entwicklung des LP-Modells geführt haben. Anschließend wird der Einfluß des zugrundeliegenden Kollektivnutzenkonzepts und des Gleichheitsprinzips auf das Modell diskutiert. Die Arbeit geht ferner auf Fragen bezüglich der benötigten Daten und des zu erwartenden Rechenaufwands ein.
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    OR spectrum 4 (1982), S. 117-117 
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    OR spectrum 4 (1982), S. 149-160 
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    Description / Table of Contents: Summary The main point of Personal Finance is the financing of proprietor's own used single-unit or doubleunit dwellings respectively owner-occupied apartments. In the following examination a mixed-integer programme for the determination of the optimum financing-mix for home construction is being developed shortly. By means of numeruous simulation tests the influence of varying capital resources of the home owner and the surplus resulting out of private life insurances upon the optimum financing structure is being analysed.
    Notes: Zusammenfassung Ein Schwerpunkt privater Finanzierungsprobleme ist die Finanzierung von Wohnungseigentum. In der folgenden Untersuchung wird zunächst ein gemischt-ganzzahliges Modell zur Ermittlung der optimalen Finanzierung von Ein- und Zweifamilienhäusern bzw. Eigentumswohnungen kurz beschrieben. Anhand zahlreicher Simulationsläufe wird der Einfluß der Variation des Eigenkapitaleinsatzes und der Überschußbeteiligung auf die optimale Finanzierungsstruktur analysiert.
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    OR spectrum 4 (1982), S. 191-191 
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    OR spectrum 4 (1982), S. 171-190 
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    Description / Table of Contents: Summary Optimal control theory treats the steering ofdynamical systems with the aim to reach a desired target. The problem of dynamic system optimization is to find the functions which will optimize a given objective functional subject to certain constraints. The purpose of the present paper is to provide an elementary approch to themaximum principle as well as to its economic interpretation. The calculation of optimal control trajectories is illustrated by some simple examples in cash management, production and investment planning, advertising and pricing, and science policy. Moreover, without claiming completeness some further applications of thedeterministic maximum principle in operations research are reviewed. The use of the maximum principle provides a significant advantage compared with dynamic programming, namely the possibility to gainqualitative insights into the structure of solution paths and thus to draw interesting economic conclusions without performing a complete analysis of the control problem.
    Notes: Zusammenfassung Die Kontrolltheorie beschäftigt sich mit der Steuerungdynamischer Systeme im Hinblick auf die Erreichung gewünschter Ziele. Das Problem der Optimierung dynamischer Systeme besteht darin, Funktionen zu finden, welche ein gegebenes Zielfunktional unter gewissen Nebenbedingungen optimieren. Zweck des vorliegenden Beitrages ist es, einen elementaren Zugang zumMaximumprinzip sowie dessen ökonomischer Interpretation zu bieten. Die Ermittlung optimaler Kontrolltrajektorien wird anhand einiger einfacher Beispiele illustriert (Kassenhaltung, Produktionsund Investitionsplanung, Werbe- und Preispolitik, Wissenschafts-Management). Ohne Vollständigkeit anzustreben, wird daneben eine Reihe weiterer Anwendungen desdeterministischen Maximumprinzips im Operations Research skizziert. Einen wesentlichen Vorteil, den das Maximumprinzip etwa im Vergleich zur dynamischen Programmierung aufweist, stellt die Möglichkeitqualitativer Einsichten in die Struktur der Lösungspfade dar, die häufig schon ohne komplette Lösung des Kontrollproblems zur Aufdeckung interessanter ökonomischer Zusammenhänge führen.
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    OR spectrum 4 (1982), S. 195-212 
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    OR spectrum 4 (1982), S. 245-245 
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    OR spectrum 4 (1982), S. 247-247 
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    OR spectrum 4 (1982), S. 246-246 
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    Mathematical programming 23 (1982), S. 1-19 
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    Keywords: Ellipsoid Algorithm ; Linear Programming ; Polynomial Boundedness ; Khachian's Method ; Linear Inequalities
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    Notes: Abstract We give some modifications of the ellipsoid algorithm for linear programming and describe a numerically stable implementation. We are concerned with practical problems where user-supplied bounds can usually be provided. Our implementation allows constraint dropping and updates bounds on the optimal value, and should be able to terminate with an indication of infeasibility or with a provably good feasible solution in a moderate number of iterations.
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    Mathematical programming 23 (1982), S. 75-86 
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    Keywords: Constrained Optimization ; Global Convergence ; Nonlinear Programming ; Penalty Function ; Quasi-Newton Method
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    Notes: Abstract The recently proposed quasi-Newton method for constrained optimization has very attractive local convergence properties. To force global convergnce of the method, a descent method which uses Zangwill's penalty function and an exact line search has been proposed by Han. In this paper a new method which adopts a differentiable penalty function and an approximate line is presented. The proposed penalty function has the form of the augmented Lagrangian function. An algorithm for updating parameters which appear in the penalty function is described. Global convergence of the given method is proved.
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    Mathematical programming 23 (1982), S. 193-205 
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    Keywords: Quasi-convexity ; Pseudo-Convexity ; Criteria
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    Notes: Abstract A first order criterion for pseudo-convexity and second order criteria for quasi-convexity and pseudo-convexity are given for twice differentiable functions on open convex sets. The relationships between these second order criteria and other known criteria are also analysed. Finally, the numbers of operations required to verify these criteria are calculated and compared.
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    Mathematical programming 23 (1982), S. 233-235 
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    Mathematical programming 23 (1982), S. 236-236 
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    Keywords: Step-Length Selection ; Linesearch ; Non-Derivative Methods
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    Notes: Abstract A step-length algorithm is an essential part of many descent methods for unconstrained and constrained optimization. In this note we present a criterion that defines an acceptable step length when only function values are available at trial step lengths.
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    Mathematical programming 24 (1982), S. 326-345 
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    Keywords: Mathematical Programming ; Convex Functions ; Quasi-concave Functions ; Lagrangian ; Saddle-Points
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    Notes: Abstract A saddle-point duality is proposed for the quasi-concave non-differentiable case of the maximization of the minimum between a finite number of functions. This class of problems contains quasi-concave (convex) programs that are known to be irreducible to convex ones. With the aid of the saddle-point duality involving conjugate-like operators, a Lagrangian is presented, the saddle-points of which give the exact global solutions. A few particular cases are discussed, among them the Von Neumann economic model and discrete rational approximation.
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    Mathematical programming 24 (1982), S. 353-355 
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    Keywords: Global Minimization ; Linear Constraints ; Quadratic Concave Function
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    Notes: Abstract A method is presented for the construction of test problems for which the global minimum point is known. Given a bounded convex polyhedron inR n , and a selected vertex, a concave quadratic function is constructed which attains its global minimum at the selected vertex. In general, this function will also have many other local minima.
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    Mathematical programming 22 (1982), S. 1-11 
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    Keywords: Graph ; Matching ; Branching ; Linear Programming
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    Notes: Abstract We introduce the concept of matching forests as a generalization of branchings in a directed graph and matchings in an undirected graph. Given special weights on the edges of a mixed graph, we present an efficient algorithm for finding an optimum weight-sum matching forest. The algorithm is a careful application of known branching and matching algorithms. The maximum cardinality matching forest problem is solved as a special case.
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    Mathematical programming 22 (1982), S. 52-70 
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    Keywords: Duality ; Graph ; Matching ; Polytope
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    Notes: Abstract The matching polytope is the convex hull of the incidence vectors of all (not necessarily perfect) matchings of a graphG. We consider here the problem of computing the dimension of the face of this polytope which contains the maximum cardinality matchings ofG and give a good characterization of this quantity, in terms of the cyclomatic number of the graph and families of odd subsets of the nodes which are always nearly perfectly matched by every maximum matching. This is equivalent to finding a maximum number of linearly independent representative vectors of maximum matchings ofG; the size of such a set is called thematching rank ofG. We also give in the last section a way of computing that rank independently of those parameters. Note that this gives us a good lower bound on the number of those matchings.
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    Mathematical programming 22 (1982), S. 288-303 
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    Keywords: TheLDL T Factorization ; Symmetric Indefinite Matrices ; Symmetric Additions of Rows and Columns ; Partial Pivoting Strategies
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    Notes: Abstract In an earlier paper [6] it is shown how the use of symmetric additions of rows and columns enables a stableLDL T factorization of symmetric indefinite matrices. In this paper we describe partial pivoting strategies. These strategies are faster than the complete pivoting strategies that were introduced in the first paper. Numerical experiments are included. The results show that some of the new strategies share the stable behaviour of complete pivoting while running almost as fast as the well-known Cholesky decomposition.
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    Mathematical programming 23 (1982), S. 87-110 
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    Keywords: Path Following ; PL Methods ; Predictor—Corrector Algorithms
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    Notes: Abstract We consider path following methods designed to trace the zeroes of a continuous or differentiable mapF:R n+1 →R n . These methods are applicable e.g. in the numerical study of nonlinear eigenvalue and bifurcation problems. Traditionally a simplicial algorithm is based on a fixed triangulationT ofR n+1 and a corresponding piecewise linear approximationF T :R n+1 →R n .4 A fixed triangulation algorithm then traces the zeroes ofF T via a complementary pivoting procedure. We present two kinds of hybrid algorithms that have the structure of a predictor—corrector method using simplicial methods to carry out the corrector steps. Numerical experience is reported showing the improvement in efficiency as compared to the fixed triangulation algorithm.
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    Mathematical programming 22 (1982), S. 350-357 
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    Keywords: 0–1 Programming ; Nonlinear Integer Programming ; Cutting Planes ; Heuristics
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    Notes: Abstract The purpose of this note is to present an accelerated algorithm for solving 0–1 positive polynomial (PP) problems. Like our covering relaxation algorithm (Management Science 1979), the accelerated algorithm is a cutting plane method, which uses the linear set covering problem as a relaxation for PP. However, a unique and novel feature of the accelerated algorithm is that it attempts to generate cutting planes from heuristic solutions to the set covering problem whenever possible. Computational results reveal that this strategy of generating cutting planes has led to a significant reduction in the computational time required to solve a PP problem.
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    Mathematical programming 22 (1982), S. 82-92 
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    Keywords: Generic Programming ; Optimality Conditions ; Nonlinear Programming
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    Notes: Abstract Optimality conditions for families of nonlinear programming problems inR n are studied from a generic point of view. The objective function and some of the constraints are assumed to depend on a parameter, while others are held fixed. Techniques of differential topology are used to show that under suitable conditions, certain strong second-order conditions are necessary for optimality except possibly for parameter values lying in a negligible set.
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    Mathematical programming 22 (1982), S. 261-287 
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    Keywords: Computational Efficiency ; Markovian Property ; Reduced Problem ; Reduced Gradient Method ; Conjugate Directions ; Quasi-Newton Method ; Quadratic Programming ; Storage Limitation ; Accuracy
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    Notes: Abstract This paper introduces the use of stochastic models for the evaluation of relative computational efficiency of algorithms. Such an approach is used for the comparison of computational efficiency of three algorithms for quadratic programming.
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    Mathematical programming 22 (1982), S. 316-331 
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    Keywords: Decomposition Algorithms ; Minimal Cut ; Flow Networks ; Lower Bounds
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    Notes: Abstract This paper provides decomposition algorithms for locating minimal cuts in a large directed network. The main theorem provides several cases for the algorithms. In the worst case, it is shown that the efficiency of one of the proposed algorithms is of the same order as a no-decomposition algorithm. As in linear programming, the obvious advantage of the proposed decomposition procedure is its ability to potentially handle larger problems than a no-decomposition algorithm.
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    Mathematical programming 23 (1982), S. 34-49 
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    Keywords: Linear Programming ; Variable Upper Bounds ; Degeneracy ; Triangular Factorization
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    Notes: Abstract Special methods for dealing with constraints of the formx j ≤ x k , called variable upper bounds, were introduced by Schrage. Here we describe a method that circumvents the massive degeneracy inherent in these constraints and show how it can be implemented using triangular basis factorizations.
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    Mathematical programming 23 (1982), S. 117-137 
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    Keywords: Polyhedral Combinatorics ; Polarity ; Blocking and Anti-blocking
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    Notes: Abstract LetX andY be finite dimensional vector spaces over the real numbers. LetΩ be a binary relation betweenX andY given by a bilinear inequality. TheΩ-polar of a subsetP ofX is the set of all elements ofY which are related byΩ to all elements ofP. TheΩ-polar of a subset ofY is defined similarly. TheΩ-polar of theΩ-polar ofP is called theΩ-closure ofP andP is calledΩ-closed ifP equals itsΩ-closure. We describe theΩ-polar of any finitely generated setP as the solution set of a finite system of linear inequalities and describe theΩ-closure ofP as a finitely generated set. TheΩ-closed polyhedra are characterized in terms of defining systems of linear inequalities and also in terms of the relationship of the polyhedronP with its recessional cone and with certain subsets ofX andY determined by the relationΩ. Six classes of bilinear inequalities are distinguished in the characterization ofΩ-closed polyhedra.
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    Mathematical programming 23 (1982), S. 181-192 
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    Keywords: Linear Complementarity Problem ; Stability ; Classes of Matrices
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    Notes: Abstract It has been shown previously that the Linear Complementarity Problem is stable when the defining matrix is positive semidefinite and when (locally) the set of solutions is nonempty and bounded. We enlarge the class of matrices for which this is true and also demonstrate how the boundedness condition leads to other stability type questions.
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    Mathematical programming 23 (1982), S. 227-232 
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    Keywords: Quadratic Bottleneck Assignment Problem ; Probabilistic Error Bounds
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    Notes: Abstract The relative error between best and worst solution of quadratic bottleneck assignment problems with cost coefficientsd ijpq =a ip b jq is considered, wherea ip is either arbitrarily given or corresponds to a distance in the plane. It is shown that the relative error is bounded by a function∈(m), tending to zero, with probability tending to one asm → ∞, provided the data are uniformly distributed. This implies that any algorithm for the above mentioned problems yields asymptotically an arbitrarily small relative error with probability tending to one.
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    Mathematical programming 23 (1982), S. 274-313 
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    Keywords: Large-Scale Optimization ; Linear Programming ; Staircase Linear Programs ; Simplex Method
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    Notes: Abstract This and a companion paper consider how current implementations of the simplex method may be adapted to better solve linear programs that have a staged, or ‘staircase’, structure. The present paper looks at ‘inversion’ routines within the simplex method, particularly those for sparse triangular factorization of a basis by Gaussian elimination and for solution of triangular linear systems. The succeeding paper examines ‘pricing’ routines. Both papers describe extensive (though preliminary) computational experience, and can point to some quite promising results.
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    Mathematical programming 24 (1982), S. 107-112 
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    Keywords: Lagrangian Subproblem ; Lagrangian Duality ; Non-linear Discrete Programming ; Separable Objective Function
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    Notes: Abstract This note presents an efficient method for the routine solution of the subproblem associated with the Lagrangian dual of discrete programming problems having separable non-linear objective function and linear constraints. An additional advantage for subgradient methods is described.
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    Mathematical programming 24 (1982), S. 113-116 
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    Mathematical programming 24 (1982), S. 117-121 
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    Mathematical programming 24 (1982), S. 137-161 
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    Keywords: Nonlinear Programming ; Exact Penalty Methods ; Successive Quadratic Programming
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    Notes: Abstract In this paper we motivate and describe an algorithm to solve the nonlinear programming problem. The method is based on an exact penalty function and possesses both global and superlinear convergence properties. We establish the global qualities here (the superlinear nature is proven in [7]). The numerical implementation techniques are briefly discussed and preliminary numerical results are given.
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    Mathematical programming 24 (1982), S. 236-240 
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    Mathematical programming 24 (1982), S. 284-313 
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    Keywords: Variational Inequality ; Complementarity ; Iterative Methods ; Convergence ; Traffic Equilibria
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    Notes: Abstract In this paper, we study both the local and global convergence of various iterative methods for solving the variational inequality and the nonlinear complementarity problems. Included among such methods are the Newton and several successive overrelaxation algorithms. For the most part, the study is concerned with the family of linear approximation methods. These are iterative methods in which a sequence of vectors is generated by solving certain linearized subproblems. Convergence to a solution of the given variational or complementarity problem is established by using three different yet related approaches. The paper also studies a special class of variational inequality problems arising from such applications as computing traffic and economic spatial equilibria. Finally, several convergence results are obtained for some nonlinear approximation methods.
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    Mathematical programming 24 (1982), S. 346-352 
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    Keywords: Least Absolute Values ; Chebychev Norm ; Regression ; Minimax ; Advanced Start ; Least Squares
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    Notes: Abstract In exploratory data analysis and curve fitting in particular, it is often desirable to observe residual values obtained with different estimation criteria. The goal with most linear model curve-fitting procedures is to minimize, in some sense, the vector of residuals. Perhaps three of the most common estimation criteria require minimizing: the sum of the absolute residuals (least absolute value or L1 norm); the sum of the squared residuals (least squares or L2 norm); and the maximum residual (Chebychev or L∞ norm). This paper demonstrates that utilizing the least squares residuals to provide an advanced start for the least absolute value and Chebychev procedures results in a significant reduction in computational effort. Computational results are provided.
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    Studia logica 41 (1982), S. 197-226 
    ISSN: 1572-8730
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    Topics: Mathematics , Philosophy
    Notes: Abstract In the first part of this paper a logic is defined for propositions whose probability of being true may not be known. A speaker's beliefs about which propositions are true are still interesting in this case. The meaning of propositions is determined by the consequences of asserting them: in this logic there are debates which incur certain costs for the protagonists. The second part of the paper describes the mathematics of the resulting logic which displays several novel features.
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    Studia logica 41 (1982), S. 227-248 
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    Topics: Mathematics , Philosophy
    Notes: Abstract The aim of this paper is to offer a rigorous explication of statements ascribing ability to agents and to develop the logic of such statements. A world is said to be feasible iff it is compatible with the actual past-and-present. W is a P-world iff W is feasible and P is true in W (where P is a proposition). P is a sufficient condition for Q iff every P world is a Q world. P is a necessary condition for Q iff Q is a sufficient condition forP. Each individual property S is shown to generate a rule for an agent X. X heeds S iff X makes all his future choices in accordance with S. (Note that X may heed S and yet fail to have it). S is a P-strategy for X iff X's heeding S together with P is a necessary and sufficient condition for X to have S. (P-strategies are thus rules which X is able to implement on the proviso P).Provisional opportunity: X has the opportunity to A provided P iff there is an S such that S is a P-strategy for X and X's implementing S is a sufficient condition for X's doing A. P is etiologically complete iff for every event E which P reports P also reports an etiological ancestry of E, and P is true. Categorical opportunity: X has the opportunity to A iff there is a P such that P is etiologically complete and X has the opportunity to A provided P. For X to have the ability to A there must not only be an appropriate strategy, but X must have a command of that strategy. X steadfastly intends A iff X intends A at every future moment at which his doing A is not yet inevitable. X has a command of S w.r.t. A and P iff X's steadfastly intending A together with P is a sufficient condition for X to implement S. Provisional ability: X can A provided P iff there is an S such that S is a P-strategy for X, X's implementing S is a sufficient condition for X's doing A, and X has a command of S w.r.t. A and P. Categorical ability: X can A iff there is a P such that P is etiologically complete and X can A provided P. X is free w.r.t. to A iff X can A and X can non- A. X is free iff there is an A such that X is free w.r.t. A.
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