Abstract and Applied Analysis
Volume 2003 (2003), Issue 11, Pages 651-670
doi:10.1155/S1085337503212094

Existence of solutions of minimization problems with an increasing cost function and porosity

Abstract

We consider the minimization problem f(x)→min, x∈K, where K is a closed subset of an ordered Banach space X and f belongs to a space of increasing lower semicontinuous functions on K. In our previous work, we showed that the complement of the set of all functions f, for which the corresponding minimization problem has a solution, is of the first category. In the present paper we show that this complement is also a σ-porous set.