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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Vydáno v:Journal of optimization theory and applications Ročník 162; číslo 2; s. 665 - 679
Hlavní autoři: Zheng, Xi Yin, Li, Runxin
Médium: Journal Article
Jazyk:angličtina
Vydáno: Boston Springer US 01.08.2014
Springer Nature B.V
Témata:
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
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Popis
Shrnutí: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.
Bibliografie:SourceType-Scholarly Journals-1
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-012-0259-3