American Institute of Mathematical Sciences

March  2020, 16(2): 511-529. doi: 10.3934/jimo.2018165

Strong vector equilibrium problems with LSC approximate solution mappings

 1 Thuongmai University, Hanoi, Vietnam 2 Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, 10307 Hanoi, Vietnam

* Corresponding author: Pham Huu Sach

Received  December 2017 Revised  June 2018 Published  October 2018

Fund Project: This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2016.11

This paper introduces two classes of parametric strong vector equilibrium problems whose approximate solution mappings are lower semicontinuous. In the first class, the objective set-valued maps satisfy some cone-convexity/cone-concavity assumptions, and in the second one, they satisfy some strongly proper cone-quasiconvexconcavity assumptions. All these mentioned concepts of generalized cone-convexity/cone-concavity/ strongly proper cone-quasiconvexconcavity are new and different from the traditional ones. Some upper semicontinuity/continuity results are also obtained. Applications to parametric weak u-set and l-set optimization problems and weak vector multivalued equilibrium problems are given.

Citation: Nguyen Ba Minh, Pham Huu Sach. Strong vector equilibrium problems with LSC approximate solution mappings. Journal of Industrial & Management Optimization, 2020, 16 (2) : 511-529. doi: 10.3934/jimo.2018165
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