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Second-order optimality conditions for efficiency in \(C^{1,1}\)-smooth quasiconvex multiobjective programming problem

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Abstract

This paper deals with a quasiconvex multiobjective programming problem with inequality and set constraints with \(C^{1,1}\)-smooth data. Based on the definition of quasiconvexity, pseudoconvexity and second-order Mordukhovich/Fréchet subdifferentials of extended-real-valued function, we propose the two generalized Ben-Tal second-order constraint qualifications and then establish strong and weak Karush-Kuhn-Tucker type second-order necessary optimality conditions for weak efficiency to such problem. Under some suitable assumptions on the pseudoconvexity and \(C^{1,1}\)-around a feasible solution of objective and constraint functions, some second-order sufficient optimality conditions in terms of Fréchet subdifferentials are presented. An application of the result on sufficient optimality of order two in terms of Mordukhovich subdifferentials in the sense of the functions belong to \(C^2\)-around a feasible solution is obtained. Some examples are also provided to demonstrate for our findings.

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Acknowledgements

The authors would like to express their sincere gratitude to anonymous reviewers for their through and helpful reviews which significantly improved the quality of the paper. Furthermore, the authors acknowledge the editors for sending our manuscript to reviewers.

Funding

Tran Van Su is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.01-2021.06.

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Authors and Affiliations

  1. Department of Mathematics, Quang Nam University, Tamky, Vietnam

    Tran Van Su

  2. Department of Basic Sciences, Thai Nguyen University of Information and Communication Technology, Thai Nguyen, Vietnam

    Dinh Dieu Hang

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  1. Tran Van Su
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  2. Dinh Dieu Hang
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Correspondence to Tran Van Su.

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The authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by both authors. The authors read and approved the final manuscript.

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Communicated by Gabriel Haeser.

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Su, T.V., Hang, D.D. Second-order optimality conditions for efficiency in \(C^{1,1}\)-smooth quasiconvex multiobjective programming problem. Comp. Appl. Math. 40, 228 (2021). https://doi.org/10.1007/s40314-021-01625-0

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  • DOI: https://doi.org/10.1007/s40314-021-01625-0

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