CHEN Wang, ZHOU Zhiang. Optimality Conditions for Set-Valued Vector Equilibrium Problems With Constraints Involving Improvement Sets[J]. Applied Mathematics and Mechanics, 2018, 39(10): 1189-1197. doi: 10.21656/1000-0887.390104
Citation: CHEN Wang, ZHOU Zhiang. Optimality Conditions for Set-Valued Vector Equilibrium Problems With Constraints Involving Improvement Sets[J]. Applied Mathematics and Mechanics, 2018, 39(10): 1189-1197. doi: 10.21656/1000-0887.390104

Optimality Conditions for Set-Valued Vector Equilibrium Problems With Constraints Involving Improvement Sets

doi: 10.21656/1000-0887.390104
Funds:  The National Natural Science Foundation of China(11431004;11471291)
  • Received Date: 2018-04-02
  • Rev Recd Date: 2018-04-09
  • Publish Date: 2018-10-01
  • The optimality conditions for setvalued vector equilibrium problems with constraints were investigated in locally convex spaces. Firstly, the concepts of the E-Henig properly efficient solution and the E-super efficient solution to the setvalued vector equilibrium problems with constraints involving improvement sets were introduced. Secondly, under the assumption of the nearly E-subconvexlikeness, the sufficient and necessary conditions for the setvalued vector equilibrium problem with constraints were established in the sense of the E-Henig proper efficiency. Finally, based on the nearly E-subconvexlikeness, the necessary conditions for the setvalued vector equilibrium problem with constraints were obtained in the sense of the E-super efficiency.
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