Optimality Conditions and Duality for Robust Nonsmooth Multiobjective Optimization Problems with Constraints

  • Jiawei Chen
  • Elisabeth KöbisEmail author
  • Jen-Chih Yao


In this paper, we investigate a robust nonsmooth multiobjective optimization problem related to a multiobjective optimization with data uncertainty. We firstly introduce two kinds of generalized convex functions, which are not necessary to be convex. Robust necessary optimality conditions for weakly robust efficient solutions and properly robust efficient solutions of the problem are established by a generalized alternative theorem and the robust constraint qualification. Further, robust sufficient optimality conditions for weakly robust efficient solutions and properly robust efficient solutions of the problem are also derived. The Mond–Weir-type dual problem and Wolfe-type dual problem are formulated. Finally, we obtain the weak, strong and converse robust duality results between the primal one and its dual problems under the generalized convexity assumptions.


Robust nonsmooth multiobjective optimization Uncertain nonsmooth multiobjective optimization Robust optimality conditions Robust duality 

Mathematics Subject Classification

65K10 90C25 



The authors are grateful to the anonymous referees, the Associate Editor and Professor Giannessi for their constructive comments and valuable suggestions, which have helped to improve the paper. This research was partially supported by the MOST 106-2923-E-039-001-MY3, the Natural Science Foundation of China (11401487), the Basic and Advanced Research Project of Chongqing (cstc2016jcyjA0239), the China Postdoctoral Science Foundation (2015M582512) and the Fundamental Research Funds for the Central Universities.


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Authors and Affiliations

  1. 1.School of Mathematics and StatisticsSouthwest UniversityChongqingChina
  2. 2.Institute of MathematicsHalle-WittenbergHalle (Saale)Germany
  3. 3.Center for General EducationChina Medical UniversityTaichungTaiwan

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