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Optimality conditions and duality in nonsmooth multiobjective optimization problems

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Abstract

Exploiting some tools of modern variational analysis involving the approximate extremal principle, the fuzzy sum rule for the Fréchet subdifferential, the sum rule for the limiting subdifferential and the scalarization formulae of the coderivatives, we establish necessary conditions for (weakly) efficient solutions of a multiobjective optimization problem with inequality and equality constraints. Sufficient conditions for (weakly) efficient solutions of an aforesaid problem are also provided by means of employing L-(strictly) invex-infine functions defined in terms of the limiting subdifferential. In addition, we introduce types of Wolfe and Mond–Weir dual problems and investigate weak/strong duality relations.

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Acknowledgments

This work was supported by a Research Grant of Pukyong National University (2014) and a grant from the NAFOSTED (Vietnam)

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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, Pusan, 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. Optimality conditions and duality in nonsmooth multiobjective optimization problems. Ann Oper Res 217, 117–136 (2014). https://doi.org/10.1007/s10479-014-1552-3

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  • DOI: https://doi.org/10.1007/s10479-014-1552-3

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