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

CHEN Wang; ZHOU Zhiang

doi:10.21656/1000-0887.390104

Volume 39 Issue 10

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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

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

doi: 10.21656/1000-0887.390104

School of Sciences, Chongqing University of Technology, Chongqing 400054, P.R.China

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

Abstract

Abstract

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.
- improvement set,
- nearly E-subconvexlikeness,
- E-Henig properly efficient solution,
- E-super efficient solution,
- optimality condition

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References(22)

References

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