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Sufficient optimality conditions and duality in vector optimization with invex-convexlike functions

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Abstract

We prove the Kuhn-Tucker sufficient optimality condition, the Wolfe duality, and a modified Mond-Weir duality for vector optimization problems involving various types of invex-convexlike functions. The class of such functins contains many known generalized convex functions. As applications, we demonstrate that, under invex-convexlikeness assumptions, the Pontryagin maximum principle is a sufficient optimality condition for cooperative differential games. The Wolfe duality is established for these games.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Hochiminh City University, Hochiminh City, Vietnam

    P. Q. Khanh (Associate Professor)

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  1. P. Q. Khanh
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Communicated by W. Stadler

The author is indebted to the referees and Professor W. Stadler for valuable remarks and comments, which have been used to revise considerably the paper.

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Khanh, P.Q. Sufficient optimality conditions and duality in vector optimization with invex-convexlike functions. J Optim Theory Appl 87, 359–378 (1995). https://doi.org/10.1007/BF02192569

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