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Weak sharp efficiency in multiobjective optimization

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Abstract

By using the generalized Fermat rule, the Mordukhovich subdifferential for maximum functions, the fuzzy sum rule for Fréchet subdifferentials and the sum rule for Mordukhovich subdifferentials, we establish a necessary optimality condition for the local weak sharp efficient solution of a constrained multiobjective optimization problem. Moreover, by employing the approximate projection theorem, and some appropriate convexity and affineness conditions, we also obtain some sufficient optimality conditions respectively for the local and global weak sharp efficient solutions of such a multiobjective optimization problem.

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Acknowledgments

The author is grateful to the two anonymous referees for their valuable comments and suggestions, which helped to improve the paper. This research was supported by the Fundamental Research Funds for the Central Universities (Grant JBK150125) and the National Natural Science Foundation of China (Grant 11171362).

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  1. Department of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, China

    S. K. Zhu

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  1. S. K. Zhu
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Zhu, S.K. Weak sharp efficiency in multiobjective optimization. Optim Lett 10, 1287–1301 (2016). https://doi.org/10.1007/s11590-015-0925-0

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