In this paper, we introduce a new condition on functions of a control problem, for which we define a KT-invex control problem. We prove that a KT-invex control problem is characterized in order that a Kuhn–Tucker point is an optimal... more
In this paper, we introduce a new condition on functions of a control problem, for which we define a KT-invex control problem. We prove that a KT-invex control problem is characterized in order that a Kuhn–Tucker point is an optimal solution. We generalize optimality results of known mathematical programming problems. We illustrate these results with examples.
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This paper is devoted to the study of relationships between solutions of Stampacchia and Minty vector variational-like inequalities, weak and strong Pareto solutions of vector optimization problems and vector critical points in Banach... more
This paper is devoted to the study of relationships between solutions of Stampacchia and Minty vector variational-like inequalities, weak and strong Pareto solutions of vector optimization problems and vector critical points in Banach spaces under pseudo-invexity and pseudo-monotonicity hypotheses. We have extended the results given by Gang and Liu (2008) [22] to Banach spaces and the relationships obtained for weak efficient points in Santos et al. (2008) [21] are completed and enabled to relate vector critical points, weak efficient points, solutions of the Minty and Stampacchia weak vector variational-like inequalities problems and solutions of perturbed vector variational-like inequalities problems.
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In this paper, we introduce new pseudoinvexity conditions on functionals involved in a multiobjective control problem, called W-KT-pseudoinvexity and W-FJ-pseudoinvexity. We prove that all Kuhn–Tucker or Fritz–John points are weakly... more
In this paper, we introduce new pseudoinvexity conditions on functionals involved in a multiobjective control problem, called W-KT-pseudoinvexity and W-FJ-pseudoinvexity. We prove that all Kuhn–Tucker or Fritz–John points are weakly efficient solutions if and only if these conditions are fulfilled. We relate weakly efficient solutions to optimal solutions of weighting control problems. We generalize recently obtained optimality results of known mathematical programming problems and control problems. We illustrate these results with an example.
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We prove that in order for the Kuhn–Tucker or Fritz John points to be efficient solutions, it is necessary and sufficient that the non-differentiable multiobjective problem functions belong to new classes of functions that we introduce... more
We prove that in order for the Kuhn–Tucker or Fritz John points to be efficient solutions, it is necessary and sufficient that the non-differentiable multiobjective problem functions belong to new classes of functions that we introduce here: KT-pseudoinvex-II or FJ-pseudoinvex-II, respectively. We illustrate it by examples. These characterizations generalize recent results given for the differentiable case. We study the dual problem and establish weak, strong and converse duality results.
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For multiobjective problems with inequality-type constraints the necessary conditions for efficient solutions are presented. These conditions are applied when the constraints do not necessarily satisfy any regularity assumptions, and they... more
For multiobjective problems with inequality-type constraints the necessary conditions for efficient solutions are presented. These conditions are applied when the constraints do not necessarily satisfy any regularity assumptions, and they are based on the concept of 2-regularity introduced by Izmailov. In general, the necessary optimality conditions are not sufficient and the efficient solution set is not the same as the Karush–Kuhn–Tucker points set. So it is necessary to introduce generalized convexity notions. In the multiobjective non-regular case we give the notion of 2-KKT-pseudoinvex-II problems. This new concept of generalized convexity is both necessary and sufficient to guarantee the characterization of all efficient solutions based on the optimality conditions.
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In this paper we introduce a new class of pseudoinvex functions for variational problems. Using this new concept, we obtain a necessary and sufficient condition for a critical point of the variational problem to be an optimal solution,... more
In this paper we introduce a new class of pseudoinvex functions for variational problems. Using this new concept, we obtain a necessary and sufficient condition for a critical point of the variational problem to be an optimal solution, illustrated with an example. Also, weak, strong and converse duality are established.
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In this paper, we introduce a new condition on functionals involved in a multiobjective control problem, for which we define the V-KT-pseudoinvex control problem. We prove that a V-KT-pseudoinvex control problem is characterized so that a... more
In this paper, we introduce a new condition on functionals involved in a multiobjective control problem, for which we define the V-KT-pseudoinvex control problem. We prove that a V-KT-pseudoinvex control problem is characterized so that a Kuhn–Tucker point is an efficient solution. We generalize recently obtained optimality results of known mathematical programming problems and control problems. We illustrate these results with an example.
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Note to users: The section "Articles in Press" contains peer reviewed accepted articles to be published in this journal. When the final article is assigned to an issue of the journal, the "Article in Press" version... more
Note to users: The section "Articles in Press" contains peer reviewed accepted articles to be published in this journal. When the final article is assigned to an issue of the journal, the "Article in Press" version will be removed from this section and will appear in the associated ...
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ABSTRACT We establish weak, strong, and converse duality results for weakly efficient solutions in vector or multiobjective variational problems, which extend and improve recent papers. For this purpose, we consider Kuhn–Tucker optimality... more
ABSTRACT We establish weak, strong, and converse duality results for weakly efficient solutions in vector or multiobjective variational problems, which extend and improve recent papers. For this purpose, we consider Kuhn–Tucker optimality conditions, weighting variational problems, and some classes of generalized convex functions, recently introduced, which are extended in this work. Furthermore, a related open question is discussed.
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Sometimes, to locate efficient solutions for multiobjective variational problems (MVPs) is quite costly, so in this paper we tackle the study of weakly efficient solutions for MVPs. A new concept of weak vector critical point which... more
Sometimes, to locate efficient solutions for multiobjective variational problems (MVPs) is quite costly, so in this paper we tackle the study of weakly efficient solutions for MVPs. A new concept of weak vector critical point which generalizes other ones already existent, and a new class of pseudoinvex functions are introduced. We will apply a new approach to prove that the
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Control problems are often applied to engineering problems; for example, control design for autonomous vehicles [1] or impulsive control problems [2]. The search for solutions in scalar and multiobjective control problems has usually been... more
Control problems are often applied to engineering problems; for example, control design for autonomous vehicles [1] or impulsive control problems [2]. The search for solutions in scalar and multiobjective control problems has usually been carried out through the study of ...