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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| Published in | Numerical functional analysis and optimization Vol. 24; no. 5-6; pp. 557 - 574 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Taylor & Francis Group
12.01.2003
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0163-0563 1532-2467 |
| DOI | 10.1081/NFA-120023868 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Jiménez, Bienvenido Novo, Vicente |
| Author_xml | – sequence: 1 givenname: Bienvenido surname: Jiménez fullname: Jiménez, Bienvenido email: bjimen1@encina.pntic.mec.es organization: Departamento de Economía e Historia Económica , Facultad de Economía y Empresa , Universidad de Salamanca – sequence: 2 givenname: Vicente surname: Novo fullname: Novo, Vicente organization: Departamento de Matemática Aplicada , E.T.S.I. Industriales, UNED |
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| Cites_doi | 10.1007/BF02193096 10.1137/S1052623498337273 10.1137/0713043 10.1007/978-3-642-46802-5_15 10.1007/978-1-4613-3326-5 10.1515/9781400873173 10.1007/s101070050083 10.1007/978-3-642-48294-6 10.1016/S0022-247X(02)00064-1 10.1137/0806010 10.1007/BF02189792 10.1007/BF00938820 10.1137/0324061 10.1007/978-3-642-02431-3 |
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| References | CIT3868-7 CIT3868-18 CIT3868-6 CIT3868-17 CIT3868-5 CIT3868-16 CIT3868-15 CIT3868-2 CIT3868-13 Novo V. (CIT3868-14) 2002 CIT3868-1 Clarke F. H. (CIT3868-4) 1983 CIT3868-10 CIT3868-20 Giorgi G. (CIT3868-9) 1992; 15 Bazaraa M. S. (CIT3868-3) 1979 Jiménez B. (CIT3868-12) 2002; 9 CIT3868-8 Hiriart-Urruty J. B. (CIT3868-11) 1996 CIT3868-19 |
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| Snippet | We study a multiobjective optimization problem in
with a feasible set defined by inequality and equality constraints and a convex set constraint. All the... |
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| SubjectTerms | Dini differentiable functions Hadamard differentiable functions Lagrange multipliers Mathematics Subject Classification: 90C29 Multiobjective optimization problems Optimality conditions for a Pareto minimum Quasiconvexity Tangent cone |
| Title | Optimality Conditions in Directionally Differentiable Pareto Problems with a Set Constraint via Tangent Cones |
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