ɛ-Subdifferentials of Set-valued Maps and ɛ-Weak Pareto Optimality for Multiobjective Optimization

A. Taa ()

Mathematical Methods of Operations Research, 2005, vol. 62, issue 2, 187-209

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 Copyright Springer-Verlag 2005

Keywords: ɛ-subdifferentials of set-valued maps; ɛ-weak Pareto; Optimality conditions; Lagrange-multipliers; Scalarization; Nearly subconvexlike; Subconvexlike; Convex; Multiobjective optimization; 90C26; 90C29; 90C46; 90C48 (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s00186-005-0007-7

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