1970•Russian Mathematical SurveysRequires access

Duality in mathematical programming and some problems of convex analysis

G. Sh. Rubinshtein

Abstract

In the paper we explain a general construction method for a problem that is dual in a certain sense to a given extremal problem and we illustrate the method by examples of various classes of problems of mathematical programming. In addition, we consider some problems in the theory of convex sets and convex functions, investigations that were stimulated chiefly by the needs of mathematical programming.

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Key concepts: Mathematics, Convex analysis, Duality (order theory), Convex optimization, Dual (grammatical number), Regular polygon, Mathematical optimization, Proper convex function