Showing papers by "William W. Cooper published in 1969"

Static and Dynamic Assignment Models with Multiple Objectives, and Some Remarks on Organization Design

Abstract: The assignment model of linear programming is here extended to allow for vector optimizations and dynamic interactions between assigned personnel and positions in each of which a variety of possible measures and approaches are explored. Formulations involving people-to-people as well as people-to-position matchings are also examined from the standpoint of organizations in which jobs may be fitted to people or vice versa as well as in weighted combinations. Possible uses of such models for dealing with the problems of placing disadvantsged or handicapped persons are noted, but the analysis stops short of the still further possibilities offered by new types of machine-technology and information systems designs.

On the theory of semi‐infinite programming and a generalization of the kuhn‐tucker saddle point theorem for arbitrary convex functions

Abstract: We first present a survey on the theory of semi-infinite programming as a generalization of linear programming and convex duality theory. By the pairing of a finite dimensional vector space over an arbitrarily ordered field with a generalized finite sequence space, the major theorems of linear programming are generalized. When applied to Euclidean spaces, semi-infinite programming theory yields a dual theorem associating as dual problems minimization of an arbitrary convex function over an arbitrary convex set in n-space with maximization of a linear function in non-negative variables of a generalized finite sequence space subject to a finite system of linear equations. We then present a new generalization of the Kuhn-Tucker saddle-point equivalence theorem for arbitrary convex functions in n-space where differentiability is no longer assumed.

A discrete probability chance-constrained capital budgeting model.

Abstract: : Aspects of the duality theory for semi-infinite programming are extended to fields with properties of non-Archimedean order. Emphasis is on nonstandard semi-infinite programming problems in Hilbert's Field. The ideas of regularization are generalized to include powers of the relative infinites in terms of the indeterminates. (Author)