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Presents prototype models of complementary pivot and fixed point theory. Information on the conversion of a linear complementary problem to a piecewise linear system; Theorems and proofs; Details on the piecewise linear maps and conjugates.

The article lists books and publications on operations research including "Operations Research: An Annotated Bibliography," 2nd edition, by James H. Batchelor, "Rational Systems and Logics of Action: The Factory Situation," by Adam Abruzzi, and "Statistical Quality Control Handbook," by Bonnie B. Small, "The Simulation of a Large-Scale Military Activity, article by Murray A. Geisler in the July 1959 issue of "Management Science."

Some simple constructive proofs are given of solutions to the matric system Mz - w = q; z ≧ 0; w ≧ 0; and zTw = 0, for various kinds of data M, q, which embrace the quadratic programming problem and the problem of finding equilibrium points of bimatrix games. The general scheme is, assuming non-degeneracy, to generate an adjacent extreme point path leading to a solution. The scheme does not require that some functional be reduced. [ABSTRACT FROM AUTHOR]

This paper describes a method of minimizing a strictly convex quadratic functional of several variables constrained by a system of linear inequalities. The method takes advantage of strict convexity by first computing the absolute minimum of the functional. In the event that the values of the variables yielding the absolute minimum do not satisfy the constraints, an equivalent and simplified quadratic problem in the `Lagrange multipliers' is derived. An efficient algorithm is devised for the transformed problem, which leads to the solution in a finite number of applications. A numerical example illustrates the method. [ABSTRACT FROM AUTHOR]