Two types of second-order dual models are formulated for a nondifferentiable minmax programming problem and usual duality results are established involving generalized type-I functions. (C) 2007 Elsevier B.V. All righ...
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Two types of second-order dual models are formulated for a nondifferentiable minmax programming problem and usual duality results are established involving generalized type-I functions. (C) 2007 Elsevier B.V. All rights reserved.
Here, we consider the minmax programming problem with a set of restrictions indexed in a compact. As a novelty, we obtain optimality criteria of the Kuhn-Tucker type involving a limited number of restrictions and prov...
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Here, we consider the minmax programming problem with a set of restrictions indexed in a compact. As a novelty, we obtain optimality criteria of the Kuhn-Tucker type involving a limited number of restrictions and prove both necessity and sufficiency under new weaker invexity assumptions. Also some dual problems are introduced and it is proved that the weak and strong duality properties hold within the same environment.
Considering the minmax programming problem, lower and upper subdifferential optimality conditions, in the sense of Mordukhovich, are derived. The approach here, mainly based on the nonsmooth dual objects of Mordukhovi...
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Considering the minmax programming problem, lower and upper subdifferential optimality conditions, in the sense of Mordukhovich, are derived. The approach here, mainly based on the nonsmooth dual objects of Mordukhovich, is completely different from that of most of the previous works where generalizations of the alternative theorem of Farkas have been applied. The results obtained are close to those known in the literature. However, one of the main achievements of this article is that we could also derive necessary optimality conditions for the minmax program of the usual Karush-Kuhn-Tucker type, which seems to be new in this field of study.
::Sufficient optimality conditions and duality results for a class of minmax programming problems are obtained under V-invexity type assumptions on objective and constraint functions. Applications of these results to ...
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In the present paper, two types of second order dual models are formulated for a minmax fractional programming problem. The concept of eta-bonvexity/generalized eta-bonvexity is adopted in order to discuss weak, stron...
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In the present paper, two types of second order dual models are formulated for a minmax fractional programming problem. The concept of eta-bonvexity/generalized eta-bonvexity is adopted in order to discuss weak, strong and strict converse duality theorems.
In this paper, the concept of second order generalized alpha-type I univexity is introduced. Based on the new definitions, we derive weak, strong and strict converse duality results for two second order duals of a min...
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In this paper, the concept of second order generalized alpha-type I univexity is introduced. Based on the new definitions, we derive weak, strong and strict converse duality results for two second order duals of a minmax fractional programming problem.
Hanson and Mend have given sets of necessary and sufficient conditions for optimality and duality in constrained optimization by introducing classes of generalized convex functions, called type I and type II functions...
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Hanson and Mend have given sets of necessary and sufficient conditions for optimality and duality in constrained optimization by introducing classes of generalized convex functions, called type I and type II functions. Recently, Bector defined univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, optimality and duality results for several mathematical programs are obtained combining the concepts of type I and univex functions. Examples of functions satisfying these conditions are given.
We present some Farkas-type results for inequality systems involving finitely many convex constraints as well as convex max-functions. Therefore we use the dual of a minmax optimization problem. The main theorem and i...
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We present some Farkas-type results for inequality systems involving finitely many convex constraints as well as convex max-functions. Therefore we use the dual of a minmax optimization problem. The main theorem and its consequences allows us to establish, as particular instances, some set containment characterizations and to rediscover two famous theorems of the alternative.
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