Optimality Conditions in Directionally Differentiable Pareto Problems with a Set Constraint via Tangent Cones

We study a multiobjective optimization problem in with a feasible set defined by inequality and equality constraints and a convex set constraint. All the involved functions are, at least, directionally differentiable. Quasiconvex inequalities are considered. Given these assumptions, an expression fo...

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Bibliographic Details
Published inNumerical functional analysis and optimization Vol. 24; no. 5-6; pp. 557 - 574
Main Authors Jiménez, Bienvenido, Novo, Vicente
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 12.01.2003
Subjects
Dini differentiable functions
Hadamard differentiable functions
Lagrange multipliers
Mathematics Subject Classification: 90C29
Multiobjective optimization problems
Optimality conditions for a Pareto minimum
Quasiconvexity
Tangent cone
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ISSN0163-0563
1532-2467
DOI10.1081/NFA-120023868

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Summary:We study a multiobjective optimization problem in with a feasible set defined by inequality and equality constraints and a convex set constraint. All the involved functions are, at least, directionally differentiable. Quasiconvex inequalities are considered. Given these assumptions, an expression for the contingent cone to the feasible set using an extended Mangasarian-Fromovitz constraint qualification is provided. As application, necessary and sufficient optimality conditions of Kuhn-Tucker type are established for a local Pareto minimal point.
ISSN:0163-0563
1532-2467
DOI:10.1081/NFA-120023868