Journal of Inequalities and Applications
Volume 2006 (2006), Article ID 54027, 14 pages
doi:10.1155/JIA/2006/54027
A generic result in vector optimization
Department of Mathematics, The Technion-Israel Institute of Technology, Haifa 32000, Israel
Received 17 November 2005; Revised 19 March 2006; Accepted 24 March 2006
Copyright © 2006 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 study a class of vector minimization problems on a complete metric space such that all its bounded closed subsets are compact. We show that for most (in the sense of Baire category) problems in the class the sets of minimal values are infinite.