Linear Programming in Reflexive Spaces

Abstract

This paper is a survey of the principal results in the theory of linear programming in reflexive linear topological spaces. We begin with a brief review of the significant results for ordinary linear programming in Euclidean space. With this as a basis for comparison, for the general case we present a complete and self-contained account of three topics: (a) the classification scheme relating the properties of primal and dual programs, (b) the duality theory relevant to the problem of duality gaps between solutions of primal and dual programs, and (c) a “marginal cost” interpretation of solutions to the dual program.