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Optimality conditions for nonsmooth multiobjective bilevel optimization problems

  • S.I.: Game theory and optimization
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Abstract

This article is devoted to the study of a nonsmooth multiobjective bilevel optimization problem, which involves the vector-valued objective functions in both levels of the considered program. We first formulate a relaxation multiobjective formulation for the multiobjective bilevel problem and examine the relationships of solutions between them. We then establish Fritz John (FJ) and Karush–Kuhn–Tucker (KKT) necessary conditions for the nonsmooth multiobjective bilevel optimization problem via its relaxation. This is done by studying a related multiobjective optimization problem with operator constraints.

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Acknowledgements

The main results of this paper were presented at the ICCOPT 2016 (Tokyo, Japan). The author would like to thank Prof. Stephan Dempe and Dr. Patrick Mehlitz for valuable comments. The author is indebted to the three referees for helpful remarks and suggestions, which greatly improved the presentation of the paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia

    Thai Doan Chuong

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  1. Thai Doan Chuong
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Correspondence to Thai Doan Chuong.

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This work was supported by the UNSW Vice-Chancellor’s Postdoctoral Research Fellowship (RG134608/SIR50).

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Chuong, T.D. Optimality conditions for nonsmooth multiobjective bilevel optimization problems. Ann Oper Res 287, 617–642 (2020). https://doi.org/10.1007/s10479-017-2734-6

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  • DOI: https://doi.org/10.1007/s10479-017-2734-6

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