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Porosity of perturbed optimization problems in Banach spaces
- Source :
-
Journal of Mathematical Analysis & Applications . Dec2006, Vol. 324 Issue 2, p751-761. 11p. - Publication Year :
- 2006
-
Abstract
- Abstract: Let X be a Banach space and Z a nonempty closed subset of X. Let be a lower semicontinuous function bounded from below. This paper is concerned with the perturbed optimization problem , denoted by -inf for . In the case when X is compactly fully 2-convex, it is proved in the present paper that the set of all points x in X for which there does not exist such that is a σ-porous set in X. Furthermore, if X is assumed additionally to be compactly locally uniformly convex, we verify that the set of all points such that the problem -inf fails to be approximately compact, is a σ-porous set in , where denotes the set of all such that . Moreover, a counterexample to which some results of Ni [R.X. Ni, Generic solutions for some perturbed optimization problem in nonreflexive Banach space, J. Math. Anal. Appl. 302 (2005) 417–424] fail is provided. [Copyright &y& Elsevier]
- Subjects :
- *COMPLEX variables
*MATHEMATICAL optimization
*BANACH spaces
*TOPOLOGY
Subjects
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 324
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 22708043
- Full Text :
- https://doi.org/10.1016/j.jmaa.2005.12.030