On stability and well-posedness in the vector optimization
We deal with vector optimization problems (f, Z), where f : X {yields} Y is a mapping, Z {improper_subset} X is a non-empty set. X and Y are metric spaces and Y is partially ordered by a non-trivial cone C. The problem (f, Z) is to find efficient points of f with respect to Z and C. We introduce a notion of level sets L(q, {epsilon}) for the problem, where q {element_of} Y and {epsilon} {>=} 0 is a real number. The level sets consist of {epsilon}-efficient points for certain values of q and of efficient points, if {epsilon} = 0. Therefore the continuity properties of the set valued mapping L are of interest and have the meaning of stability of the underlying problem. We give some sufficient conditions for Kuratowski-convergency of level sets to a certain set L(q, 0). Further, we suggest an approach towards well-posedness in the vector optimization. Notions of well-posedness in Tykhonov sense and strong well-posedness are introduced. Some results are presented, which establish similar characterizations of the well-posed vector optimization problems are they are known for scalar problems. Variational principles with well-posed perturbed functions are formulated.
- OSTI ID:
- 35944
- Report Number(s):
- CONF-9408161-; TRN: 94:009753-0210
- Resource Relation:
- Conference: 15. international symposium on mathematical programming, Ann Arbor, MI (United States), 15-19 Aug 1994; Other Information: PBD: 1994; Related Information: Is Part Of Mathematical programming: State of the art 1994; Birge, J.R.; Murty, K.G. [eds.]; PB: 312 p.
- Country of Publication:
- United States
- Language:
- English
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