Necessary and sufficient condiitions for multiobjective optimization problems

We consider the following multiobjective optimization problem (P) Minimize F(x) subject to x ∈ X where Fis a set-valued map between two Banach X and Y. When the set-valued map F is upper somedifferentiable and compact Luc [2] gives necessary and sufficient optimality conditions for (P) in terms of c...

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Published in:Optimization Vol. 36; no. 2; pp. 97 - 104
Main Author: Taa, A.
Format: Journal Article
Language:English
Published: Gordon and Breach Science Publishers 01.01.1996
Subjects:
Compact Base
Contingent Derivative
Multiobjective Optimization Problem
Pareto Minimal Point
S-Derivative
Set-Valued Map
ISSN:0233-1934, 1029-4945
Online Access:Get full text
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Abstract We consider the following multiobjective optimization problem (P) Minimize F(x) subject to x ∈ X where Fis a set-valued map between two Banach X and Y. When the set-valued map F is upper somedifferentiable and compact Luc [2] gives necessary and sufficient optimality conditions for (P) in terms of contingent derivatives. In this paper we study the same problem under weaker notion of set-valued derivatives and without nether compactness nor upper somedifferentiability assumptions
AbstractList We consider the following multiobjective optimization problem (P) Minimize F(x) subject to x ∈ X where Fis a set-valued map between two Banach X and Y. When the set-valued map F is upper somedifferentiable and compact Luc [2] gives necessary and sufficient optimality conditions for (P) in terms of contingent derivatives. In this paper we study the same problem under weaker notion of set-valued derivatives and without nether compactness nor upper somedifferentiability assumptions
Author Taa, A.
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Cites_doi 10.1007/BF00940634
10.1007/BF00939554
10.1007/BF01594928
10.1137/0322033
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Snippet We consider the following multiobjective optimization problem (P) Minimize F(x) subject to x ∈ X where Fis a set-valued map between two Banach X and Y. When...
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SubjectTerms Compact Base
Contingent Derivative
Multiobjective Optimization Problem
Pareto Minimal Point
S-Derivative
Set-Valued Map
Title Necessary and sufficient condiitions for multiobjective optimization problems
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