Accession Number : AD0707576

Title :   SUFFICIENCY CONDITIONS AND A DUALITY THEORY FOR MATHEMATICAL PROGRAMMING PROBLEMS IN ARBITRARY LINEAR SPACES.

Corporate Author : UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES ELECTRONIC SCIENCES LAB

Personal Author(s) : Neustadt,Lucien W.

Report Date : 1970

Pagination or Media Count : 28

Abstract : The paper is devoted to an investigation of mathematical programming problems in arbitrary linear vector spaces. Two cases are considered: problems with a scalar-valued criterion function, and minimax problems. The constraints of the problem are assumed to be of three types: (a) the point must belong to a given (arbitrary) convex set in the underlying linear space, (b) a finite-dimensional equality constraint must be satisfied, (c) a generalized (possibly infinite-dimensional) inequality constraint, defined in terms of a convex body in a linear topological space, must be satisfied. Assuming that the equality constraints are affine, the the 'inequality' contraints are, in a certain generalized sense, convex, and that the problem is 'well-posed', Kuhn-Tucker type conditions which are both necessary and sufficient for optimality are obtained. A duality theory for obtaining the 'multipliers' in the generalized Kuhn-Tucker conditions is presented. An application to optimal control theory is also presented. (Author)

Descriptors :   (*MATHEMATICAL PROGRAMMING, VECTOR SPACES), CONVEX SETS, TOPOLOGY, BOUNDARY VALUE PROBLEMS, MINIMAX TECHNIQUE, INEQUALITIES, ALGORITHMS, CONTROL SYSTEMS

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE