向量和集两种标准下集值优化近似解的最优性条件

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Optimality Conditions for Approximate Solutions of Set-ValuedOptimization under Two Criteria of Vector and Set

KONG Xiangyu¹, YU Guolin¹, ZHANG Yinfeng¹, LIU Sanyang²

1. Institute of Applied Mathematics, Beifang University of Nationalities, Yinchuan 750021, China;2. School of Mathematics and Statistics, Xidian University, Xi’an 710071, China

Received:2016-10-09 Online:2017-09-26 Published:2017-09-26
Contact: KONG Xiangyu E-mail:kxywz08@163.com

Abstract

Abstract: We considered the optimality conditions for a class of setvalued optimization problems with respect to approximate solutions under two criteria of vector optimization and set optimization. We obtained the necessary and sufficient conditions for optimality of setvalued optimization problems with respect to approximate solutions under two criteria of vector optimization and set optimization by using upper and lower Studniarski derivatives.

Key words: optimality condition, vector optimization, peudoconvexity, Studniarski derivative, set optimization

CLC Number:

O224.1

KONG Xiangyu, YU Guolin, ZHANG Yinfeng, LIU Sanyang. Optimality Conditions for Approximate Solutions of Set-ValuedOptimization under Two Criteria of Vector and Set[J].Journal of Jilin University Science Edition, 2017, 55(05): 1095-1100.

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Optimality Conditions for Approximate Solutions of Set-ValuedOptimization under Two Criteria of Vector and Set

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