Generic Existence of Solutions of Symmetric Optimization Problems

Abstract

In this paper we study a class of symmetric optimization problems which is identified with a space of objective functions, equipped with an appropriate complete metric. Using the Baire category approach, we show the existence of a subset of the space of functions, which is a countable intersection of open and everywhere dense sets, such that for every objective function from this intersection the corresponding symmetric optimization problem possesses a solution.

Keywords

• complete metric space
• generic element
• lower semicontinuos function
• uniformity