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On approximate solutions of nondifferentiable vector optimization problems with cone-convex objectives

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Abstract

In this paper, we study a nondifferentiable constrained vector optimization problem where the partial order in the image space is induced by a closed, convex and pointed cone with nonempty interior. Under the C-convexity assumption, we present necessary and sufficient KKT optimality conditions for weakly C-\(\epsilon \)-efficient solutions. In addition, we formulate a Wolfe-type dual problem, and then weak and strong duality theorems are presented.

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Acknowledgements

The authors would like to express their sincere thanks to anonymous referees for valuable suggestions and comments for the paper. The first and third authors were supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2016R1A2B4011589). The second author was supported by Natural Science Foundation of Jilin Province (no. 20180101215JC).

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Authors and Affiliations

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

    Zhe Hong & Do Sang Kim

  2. Department of Mathematics, Yanbian University, Yanji City, 133002, China

    Guang-Ri Piao

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  1. Zhe Hong
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  2. Guang-Ri Piao
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  3. Do Sang Kim
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Correspondence to Do Sang Kim.

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Hong, Z., Piao, GR. & Kim, D.S. On approximate solutions of nondifferentiable vector optimization problems with cone-convex objectives. Optim Lett 13, 891–906 (2019). https://doi.org/10.1007/s11590-018-1292-4

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