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Characterizations of efficient and weakly efficient points in nonconvex vector optimization

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Abstract

In this paper, a class of nonconvex vector optimization problems with inequality constraints and a closed convex set constraint are considered. By means of Clarke derivatives and Clarke subdifferentials, a necessary and sufficient condition of weak efficiency and a sufficient criteria of efficiency are presented under suitable generalized convexity. A special case is discussed in finite dimensional space and an equivalent version of sufficient criteria of efficiency is obtained by means of Clarke derivative and linearizing cone. Some examples also are given to illustrate the main results.

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Acknowledgments

This work is partially supported by the National Natural Science Foundation of China (Grants 11301574, 11271391, 11171363), the Natural Science Foundation Project of Chongqing (Grant 2011BA0030), the Natural Science Foundation Project of Chongqing (Grant CSTC2012jjA00002) and the Research Fund for the Doctoral Program of Chongqing Normal University (13XLB029).

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  1. College of Mathematics Science, Chongqing Normal University, Chongqing, 401331, China

    Ke Quan Zhao & Xin Min Yang

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  1. Ke Quan Zhao
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  2. Xin Min Yang
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Correspondence to Ke Quan Zhao.

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Zhao, K.Q., Yang, X.M. Characterizations of efficient and weakly efficient points in nonconvex vector optimization. J Glob Optim 61, 575–590 (2015). https://doi.org/10.1007/s10898-014-0191-1

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