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Optimality and Duality in Nonsmooth Conic Vector Optimization

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Abstract

This article is concerned with a nonsmooth vector optimization problem involving conic constraints. We employ some advanced tools of variational analysis and generalized differentiation to establish necessary conditions for (weakly) efficient solutions of the conic vector optimization problem, where the fuzzy necessary condition and sequential necessary condition are expressed in terms of the Fréchet subdifferential and the exact necessary condition is in terms of the limiting/Mordukhovich subdifferential of the related functions. Sufficient conditions for (weakly) efficient solutions of the underlying problem are also provided by means of introducing the concepts of (strictly) generalized convex vector functions with respect to a cone. In addition, we propose a dual problem to the conic vector optimization problem and explore weak, strong, and converse duality relations between these two problems.

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Acknowledgements

The author would like to thank three anonymous referees for the valuable comments and suggestions.

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Authors and Affiliations

  1. Optimization and Applications Research Group, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Thai Doan Chuong

  2. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Thai Doan Chuong

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  1. Thai Doan Chuong
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Correspondence to Thai Doan Chuong.

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Johannes O. Royset.

Dedicated to Professor Boris S. Mordukhovich on the occasion of his 70th birthday.

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Chuong, T.D. Optimality and Duality in Nonsmooth Conic Vector Optimization. J Optim Theory Appl 183, 471–489 (2019). https://doi.org/10.1007/s10957-019-01577-w

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  • DOI: https://doi.org/10.1007/s10957-019-01577-w

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