×

zbMATH — the first resource for mathematics

Essential weak efficient solution in multiobjective optimization problems. (English) Zbl 0753.90058
The concept of essential weak solution in multiobjective optimization problems is introduced. We prove that most of the multiobjective optimization problems (in the sense of Baire category) are almost essential (i.e., they have at least one essential weakly efficient solution) or essential (i.e., their weakly efficient solutions are all essential).
Reviewer: J.Yu

MSC:
90C29 Multi-objective and goal programming
54C60 Set-valued maps in general topology
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Beer, G, On a generic optimization theorem of Kenderov, Nonlinear anal. theory, methods, appl., 6, 647-655, (1988) · Zbl 0686.90042
[2] Christensen, J.P.R, Theorems of namioka and Johnson type for upper semi-continuous and compact valued setvalued mappings, (), 649-655 · Zbl 0506.54016
[3] Engleking, R, General topology, (1977), Polish Scientific Warsaw
[4] Fort, M.K, Points of continuity of semicontinuous functions, Publ. math. debrecen, 2, 100-102, (1951) · Zbl 0044.05703
[5] Kenderov, P.S, Most of the optimization problems have unique solution, (), 203-216 · Zbl 0541.49006
[6] Klein, E; Thompson, A, Theory of correspondences, (1984), Wiley New York
[7] Luc, D.T, Theory of vector optimization, () · Zbl 0923.49012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.