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

Xi Yin Zheng () and Runxin Li
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Xi Yin Zheng: Yunnan University
Runxin Li: Yunnan University

Journal of Optimization Theory and Applications, 2014, vol. 162, issue 2, No 18, 665-679

Abstract: 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.

Keywords: Vector optimization; Proximal normal cone; Coderivative; Weak-approximate-Pareto solution (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10957-012-0259-3

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