Approximate Fenchel-Lagrangian Duality for Constrained Set-Valued Optimization Problems


Hai-Jun Wang;Cao-Zong Cheng;Xiao-Dong Fan;


In this article, we construct a Fenchel-Lagrangian ε-dual problem for set-valued optimization problems by using the perturbation methods. Some relationships between the solutions of the primal and the dual problems are discussed. Moreover, an ε-saddle point theorem is proved.


Set-valued optimization; ε-conjugate map; ε-weak efficiency; ε-weak saddle point


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Total: 18 articles

  • [1] CHENG Yong-hong School of Management, Fudan University, Shanghai 200433,China, Existence of Solutions for Vector Equilibrium Problems with Set-valued Mappings, Acta Analysis Functionalis Applicata,
  • [2] Zhong-Fei Li;;Guang-Ya Chen, Lagrangian Multipliers, Saddle Points, and Duality in Vector Optimization of Set-Valued Maps, Journal of Mathematical Analysis and Applications,
  • [3] S.J. Li;;C.R. Chen;;S.Y. Wu, Conjugate dual problems in constrained set-valued optimization and applications, European Journal of Operational Research,
  • [4] T. Tanino;;Y. Sawaragi, Conjugate maps and duality in multiobjective optimization, Journal of Optimization Theory and Applications,


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