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Optimality conditions for vector equilibrium problems with constraint in Banach spaces

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Abstract

In this paper, vector equilibrium problems with constraint in Banach spaces are investigated. Kuhn–Tucker-like conditions for weakly efficient solutions are given by using the Gerstewitz’s function and nonsmooth analysis. Moreover, the sufficient conditions of weakly efficient solutions are established under the assumption of generalized invexity. As applications, necessary conditions of weakly efficient solutions for vector variational inequalities with constraint and vector optimization problems with constraint are obtained.

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Acknowledgments

This research was supported by the Natural Science Foundation of Zhejiang Province (LY12A01005, LY13A010006).

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  1. Department of Mathematics, Zhejiang Normal University, Jinhua , 321004, Zhejiang, China

    Yanyan Feng & Qiusheng Qiu

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  1. Yanyan Feng
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  2. Qiusheng Qiu
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Correspondence to Qiusheng Qiu.

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Feng, Y., Qiu, Q. Optimality conditions for vector equilibrium problems with constraint in Banach spaces. Optim Lett 8, 1931–1944 (2014). https://doi.org/10.1007/s11590-013-0695-5

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