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Lagrange Multiplier Rules for Weak Approximate Pareto Solutions of Constrained Vector Optimization Problems in Hilbert Spaces

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Abstract

In the Hilbert space case, in terms of proximal normal cone and proximal coderivative, we establish a Lagrange multiplier rule for weak approximate Pareto solutions of constrained vector optimization problems. In this case, our Lagrange multiplier rule improves the main result on vector optimization in Zheng and Ng (SIAM J. Optim. 21: 886–911, 2011). We also introduce a notion of a fuzzy proximal Lagrange point and prove that each Pareto (or weak Pareto) solution is a fuzzy proximal Lagrange point.

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Acknowledgements

The research was supported by the National Natural Science Foundation of P.R. China (Grant No. 10761012), IRTSTYN and the Yunnan University Graduate Research Fund (ynuy201141).

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  1. Department of Mathematics, Yunnan University, Kunming, 650091, P.R. China

    Xi Yin Zheng & Runxin Li

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  1. Xi Yin Zheng
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  2. Runxin Li
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Correspondence to Xi Yin Zheng.

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Zheng, X.Y., Li, R. Lagrange Multiplier Rules for Weak Approximate Pareto Solutions of Constrained Vector Optimization Problems in Hilbert Spaces. J Optim Theory Appl 162, 665–679 (2014). https://doi.org/10.1007/s10957-012-0259-3

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  • DOI: https://doi.org/10.1007/s10957-012-0259-3

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