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

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...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 162; no. 2; pp. 665 - 679
Main Authors: Zheng, Xi Yin, Li, Runxin
Format: Journal Article
Language:English
Published: Boston Springer US 01.08.2014
Springer Nature B.V
Subjects:
Analysis
Applications of Mathematics
Approximation
Calculus of Variations and Optimal Control; Optimization
Engineering
Fuzzy
Fuzzy logic
Hilbert space
Lagrange multiplier
Lagrange multipliers
Mathematical analysis
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Pareto optimality
Studies
Theory of Computation
Topological manifolds
Vector space
Vectors (mathematics)
Weak-approximate-Pareto solution
Coderivative
Vector optimization
Proximal normal cone
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary: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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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-012-0259-3