Allen L. Soyster

A mathematical programming approach for determining oligopolistic market equilibrium

During the past several years it has become increasingly common to use mathematical programming methods for deriving economic equilibria of supply and demand. Well-defined approaches exist for the case of a single firm (monopoly) and for the case of many firms (perfect competition). In this paper a certain family of convex programs is formulated to determine equilibria for the case of a few firms (oligopoly). Solutions to this family of convex programs are shown to be Nash equilibria in the formal sense ofN person games. This equivalence leads to a mathematical programming-based algorithm for determining an oligopolistic market equilibrium.

Stackelberg-Nash-Cournot Equilibria: Characterizations and Computations

A rotor for exchangers in which the thermodynamic characteristics of two gas currents are transferred from one current to the other while they are being passed through the exchanger insert in zones separated from one another, said rotor being formed with sector spaces defined by the outer surface of an inner hub, an outer envelope and radial spokes interconnecting said hub with said envelope, which sector spaces are filled with a moisture and/or heat transferring insert formed as prefabricated units having the shape of the sector spaces.

Modeling and integer programming techniques applied to propositional calculus

Abstract This paper discusses alternative methods for constructing a 0–1 integer programming problem from a propositional calculus problem and the use of the resulting mathematical program to solve the related logic problem. This paper also identifies some special structures associated with the constraint sets and discusses several fundamental results concerning methods of preprocessing the logical inferences into constraints.

Electric Utility Capacity Expansion Planning with Uncertain Load Forecasts

Abstract This paper is concerned with the role and impact of uncertainty in the forecast of electricity demand. In particular, the emphasis is upon how uncertainty about future demand affects current choices and strategies of capacity expansion. The uncertainty in demand is incorporated into both a stochastic linear program with recourse and an ordinary linear program. In the latter case only the “expected value” of demand is considered. The main result of this paper is that under fairly general conditions an ordinary linear program provides the same optimal solution as the more complex stochastic linear program.

Discriminant analysis via mathematical programming: certain problems and their causes

Abstract In the past several years there has been some interest shown in the use of mathematical programming (i.e. specifically either linear programming or linear goal programming) for use in discriminant analysis—an area previously approached only by the more conventional methods of statistical analysis. However, those who have actually attempted to apply the mathematical programming approach have, in some instances, encountered a number of problems which raise questions about the usefulness of the methodology in such an application. In this paper, we describe these problems, identify their causes and suggest ways in which such problems may be avoided. This work represents an ongoing effort on the part of the authors in the development of an efficient revised approach to discriminant analysis via mathematical programming.

Technical Note—A Duality Theory for Convex Programming with Set-Inclusive Constraints

This paper extends the notion of convex programming with set-inclusive constraints as set forth by Soyster [Opns. Res. 21, 1154–1157 (1973)] by replacing the objective vector c with a convex set C and formulating a dual problem. The primal problem to be considered is \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document}

Generating logical expressions from positive and negative examples via a branch-and-bound approach

\sup\Bigl\{\inf_{c\in C} c \cdot x \mid x_{1}K_{1}+x_{2}K_{2}+ \ldots x_{n}K_{n}\subseteq K(b), x_{i}\geq 0\Bigr\}

An approach to guided learning of boolean functions

\end{document} where the sets {Kj} are convex activity sets, K(b) is a polyhedral resource set, C is a convex set of objective vectors, and the binary operation + refers to addition of sets. Any feasible solution to the dual problem provides an upper bound to (I) and, at optimality conditions, the value of (I) is equal ...