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Optimality conditions in convex optimization with locally Lipschitz constraints

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Abstract

In this paper, we consider a convex optimization problem with locally Lipschitz inequality constraints. The KKT optimality conditions (both necessary and sufficient) for quasi \(\epsilon \)-solutions are established under Slater’s constraint qualification and a non-degeneracy condition. Moreover, we explore the optimality condition for weakly efficient solutions in multiobjective convex optimization involving locally Lipschitz constraints. Some examples are given to illustrate our results.

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Acknowledgements

The authors would like to express their sincere thanks to anonymous referees for helpful suggestions and valuable comments for the paper. This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2016R1A2B4011589).

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Authors and Affiliations

  1. Department of Applied Mathematics, Pukyong National University, Busan, 48513, Korea

    Zhe Hong, Kwan Deok Bae & Do Sang Kim

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  1. Zhe Hong
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  2. Kwan Deok Bae
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  3. Do Sang Kim
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Correspondence to Do Sang Kim.

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Hong, Z., Bae, K.D. & Kim, D.S. Optimality conditions in convex optimization with locally Lipschitz constraints. Optim Lett 13, 1059–1068 (2019). https://doi.org/10.1007/s11590-018-1343-x

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  • DOI: https://doi.org/10.1007/s11590-018-1343-x

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