Nonsmooth Semi-infinite Multiobjective Optimization Problems

We apply some advanced tools of variational analysis and generalized differentiation to establish necessary conditions for (weakly) efficient solutions of a nonsmooth semi-infinite multiobjective optimization problem (SIMOP for brevity). Sufficient conditions for (weakly) efficient solutions of a SI...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 160; no. 3; pp. 748 - 762
Main Authors: Chuong, Thai Doan, Kim, Do Sang
Format: Journal Article
Language:English
Published: Boston Springer US 01.03.2014
Springer Nature B.V
Subjects:
Analysis
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Constraining
Convex analysis
Convexity
Differentiation
Engineering
Mathematical functions
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Studies
Theory of Computation
Optimality condition
Duality
Limiting/Mordukhovich subdifferential
Approximate extremal principle
Semi-infinite optimization
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:We apply some advanced tools of variational analysis and generalized differentiation to establish necessary conditions for (weakly) efficient solutions of a nonsmooth semi-infinite multiobjective optimization problem (SIMOP for brevity). Sufficient conditions for (weakly) efficient solutions of a SIMOP are also provided by means of introducing the concepts of (strictly) generalized convex functions defined in terms of the limiting subdifferential of locally Lipschitz functions. In addition, we propose types of Wolfe and Mond–Weir dual problems for SIMOPs, and explore weak and strong duality relations under assumptions of (strictly) generalized convexity. Examples are also designed to analyze and illustrate the obtained results.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-013-0314-8