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Nonsmooth Semi-infinite Multiobjective Optimization Problems

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Abstract

We apply some advanced tools of variational analysis and generalized differentiation to establish necessary conditions for (weakly) efficient solutions of a nonsmooth semi-infinite multiobjective optimization problem (SIMOP for brevity). Sufficient conditions for (weakly) efficient solutions of a SIMOP are also provided by means of introducing the concepts of (strictly) generalized convex functions defined in terms of the limiting subdifferential of locally Lipschitz functions. In addition, we propose types of Wolfe and Mond–Weir dual problems for SIMOPs, and explore weak and strong duality relations under assumptions of (strictly) generalized convexity. Examples are also designed to analyze and illustrate the obtained results.

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Authors and Affiliations

  1. Department of Mathematics & Applications, Saigon University, 273 An Duong Vuong Street, Ward 3, District 5, Ho Chi Minh City, Vietnam

    Thai Doan Chuong

  2. Department of Applied Mathematics, Pukyong National University, Busan, 608-737, Korea

    Do Sang Kim

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  1. Thai Doan Chuong
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  2. Do Sang Kim
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Correspondence to Do Sang Kim.

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Chuong, T.D., Kim, D.S. Nonsmooth Semi-infinite Multiobjective Optimization Problems. J Optim Theory Appl 160, 748–762 (2014). https://doi.org/10.1007/s10957-013-0314-8

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  • DOI: https://doi.org/10.1007/s10957-013-0314-8

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