SUFFICIENCY CONDITIONS AND A DUALITY THEORY FOR MATHEMATICAL PROGRAMMING PROBLEMS IN ARBITRARY LINEAR SPACES.
UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES ELECTRONIC SCIENCES LAB
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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
- Operations Research