
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 scalarvalued 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 finitedimensional equality constraint must be satisfied, (c) a generalized (possibly infinitedimensional) 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 'wellposed', KuhnTucker type conditions which are both necessary and sufficient for optimality are obtained. A duality theory for obtaining the 'multipliers' in the generalized KuhnTucker 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