
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 pointtoset 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 mvector. Previous work by Evans and Gould, Greenberg and Pierskalla, and others has established necessary and sufficient conditions for this map to be upper semicontinuous or lower semicontinuous. 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 epsilonoptimal 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