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
Department of Mathematics, The Technion—Israel Institute of Technology, Haifa 32000, Israel
Received 18 July 2002
Copyright © 2003 Alexander J. Zaslavski. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.