ɛ-Subdifferentials of Set-valued Maps and ɛ-Weak Pareto Optimality for Multiobjective Optimization |
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Authors: | A Taa |
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Institution: | (1) Département de Mathématiques, Faculté des Sciences et Techniques, B. P. 549 Marrakech, Morocco |
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Abstract: | In this paper we consider vector optimization problems where objective and constraints are set-valued maps. Optimality conditions
in terms of Lagrange-multipliers for an ɛ-weak Pareto minimal point are established in the general case and in the case with
nearly subconvexlike data. A comparison with existing results is also given. Our method used a special scalarization function,
introduced in optimization by Hiriart-Urruty. Necessary and sufficient conditions for the existence of an ɛ-weak Pareto minimal
point are obtained. The relation between the set of all ɛ-weak Pareto minimal points and the set of all weak Pareto minimal
points is established. The ɛ-subdifferential formula of the sum of two convex functions is also extended to set-valued maps
via well known results of scalar optimization. This result is applied to obtain the Karush–Kuhn–Tucker necessary conditions,
for ɛ-weak Pareto minimal points |
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Keywords: | ɛ -subdifferentials of set-valued maps ɛ -weak Pareto Optimality conditions Lagrange-multipliers Scalarization Nearly subconvexlike Subconvexlike Convex Multiobjective optimization |
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