Global stability of optimization problems

Abstract

This paper presents necessary and sufficient conditions for the stability of the problem . Here M is a subset of a metric space X, λ is an element of some set ⋀ “with convergence” and f is a functional defined on the Cartesian product X×⋀. These conditions apply to the upper and lower semiconformity of the function and the upper semiconformity of the point-to-set mapping . The used set-convergence is less strong than the convergence induced by the Hausdorff metric. As conclusions theorems on the relationship between the f 0 and [fcirc] upper semiconformity and sufficient stability-conditions for some general problems (especially quasi convex programming) are received. The necessity of certain suppositions is illustrated by appropriate examples.