Second-order conditions for nonsmooth multiobjective optimization problems with inclusion constraints |
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Authors: | Ahmed Taa |
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Institution: | 1.Département de Mathématiques,Faculté des Sciences et Techniques,Marrakech,Morocco |
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Abstract: | This paper investigates second-order optimality conditions for general multiobjective optimization problems with constraint
set-valued mappings and an arbitrary constraint set in Banach spaces. Without differentiability nor convexity on the data
and with a metric regularity assumption the second-order necessary conditions for weakly efficient solutions are given in
the primal form. Under some additional assumptions and with the help of Robinson -Ursescu open mapping theorem we obtain dual
second-order necessary optimality conditions in terms of Lagrange-Kuhn-Tucker multipliers. Also, the second-order sufficient
conditions are established whenever the decision space is finite dimensional. To this aim, we use the second-order projective
derivatives associated to the second-order projective tangent sets to the graphs introduced by Penot. From the results obtained
in this paper, we deduce and extend, in the special case some known results in scalar optimization and improve substantially
the few results known in vector case. |
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