The Ekeland variational principle for Henig proper minimizers and super minimizers |
| |
Authors: | Truong Xuan Duc Ha |
| |
Affiliation: | Institute of Mathematics, 18 Hoang Quoc Viet Road, 10307 Hanoi, Viet Nam |
| |
Abstract: | In this paper we consider, for the first time, approximate Henig proper minimizers and approximate super minimizers of a set-valued map F with values in a partially ordered vector space and formulate two versions of the Ekeland variational principle for these points involving coderivatives in the sense of Ioffe, Clarke and Mordukhovich. As applications we obtain sufficient conditions for F to have a Henig proper minimizer or a super minimizer under the Palais-Smale type conditions. The techniques are essentially based on the characterizations of Henig proper efficient points and super efficient points by mean of the Henig dilating cones and the Hiriart-Urruty signed distance function. |
| |
Keywords: | Ekeland variational principle Vector optimization Henig proper minimizer Super minimizer Henig dilating cone Cone with base Set-valued map Coderivative |
本文献已被 ScienceDirect 等数据库收录! |