Accession Number : AD0767978

Title :   Stability and Convergence in Mathematical Programming.

Descriptive Note : Research rept.,

Corporate Author : CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER

Personal Author(s) : Topkis,Donald M. ; Stern,Michael H.

Report Date : SEP 1973

Pagination or Media Count : 40

Abstract : The authors consider the point-to-set map (S sub b) = (x / g(x) < or = b), where g(.) is a function from (E sup n) to (E sup m) and b is an m-vector. Previous work by Evans and Gould, Greenberg and Pierskalla, and others has established necessary and sufficient conditions for this map to be upper semi-continuous or lower semi-continuous. Here the authors consider the stronger notion of linear continuity, which requires that changes in (S sub b) as a function of b satisfy a Lipshitz condition. Necessary conditions are presented for which (S sub b) has this property. The authors then consider the class of problems of maximizing a function over (S sub b) and give conditions under which the optimal values of the objective function satisfies a Lipshitz condition in terms of b. Conditions are also given for the sets of epsilon-optimal solutions to be linearly continuous in b. Both convex and nonconvex problems are considered. Some extensions are made to functional perturbations and other areas. (Author)

Descriptors :   (*MATHEMATICAL PROGRAMMING, CONVERGENCE), STABILITY, LINEAR PROGRAMMING, MAPPING(TRANSFORMATIONS), CONVEX SETS, THEOREMS, OPTIMIZATION

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE