Optimality conditions and duality on approximate solutions in vector optimization with arcwise connectivity

Optimality conditions and duality on approximate solutions in vector optimization with arcwise connectivity

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Article ID: iaor20127287
Volume: 6
Issue: 8
Start Page Number: 1613
End Page Number: 1626
Publication Date: Dec 2012
Journal: Optimization Letters
Authors: , ,
Keywords: vector optimization
Abstract:

In this paper a new class of generalized vector‐valued arcwise connected functions, termed sub‐arcwise connected functions, is introduced. The properties of sub‐arcwise connected functions are derived. The approximate quasi efficient solutions of vector optimization problems are studied, and the necessary and sufficient optimality conditions are obtained under the assumption of arcwise connectivity. An approximate Mond‐Weir type dual problem is formulated and the duality theorems are established.

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