M. Arana-Jiménez

KT-invex control problem

Abstract 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.

Weak efficiency in multiobjective variational problems under generalized convexity

In this paper, we provide new pseudoinvexity conditions on the involved functionals of a multiobjective variational problem, such that all vector 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 problems. We improve recent papers, and we generalize pseudoinvexity conditions used in multiobjective mathematical programming, so as some of their characterization results. The new conditions and results are illustrated with an example.

A characterization of pseudoinvexity in multiobjective programming

In this paper, we introduce new classes of vector functions which generalize the class of scalar invex functions. We prove that these new classes of vector functions are characterized in such a way that every vector critical point is an efficient solution of a Multiobjective Programming Problem. We establish relationships between these new classes of functions and others used in the study of efficient and weakly efficient solutions.

FJ-Invex control problem

Abstract This paper introduces a new condition on the functionals of a control problem and extends a recent characterization result of KT-invexity. We prove that the new condition, the FJ-invexity, is both necessary and sufficient in order to characterize the optimal solution set using Fritz John points.

Duality and a Characterization of Pseudoinvexity for Pareto and Weak Pareto Solutions in Nondifferentiable Multiobjective Programming

In this paper, we unify recent optimality results under directional derivatives by the introduction of new pseudoinvex classes of functions, in relation to the study of Pareto and weak Pareto solutions for nondifferentiable multiobjective programming problems. We prove that in order for feasible solutions satisfying Fritz John conditions to be Pareto or weak Pareto solutions, it is necessary and sufficient that the nondifferentiable multiobjective problem functions belong to these classes of functions, which is illustrated by an example. We also study the dual problem and establish weak, strong, and converse duality results.

Generalized convexity in fuzzy vector optimization through a linear ordering

In this article we study efficiency and weakly efficiency in fuzzy vector optimization. After formulating the problem, we introduce two new concepts of generalized convexity for fuzzy vector mappings based on the generalized Hukuhara differentiability, pseudoinvexity-I and pseudoinvexity-II. We prove that pseudoinvexity is the necessary and sufficient condition for a stationary point to be a solution of a fuzzy vector optimization problem. We give conditions to insure that a fuzzy vector mapping is invex and pseudoinvex (I and II). Moreover, we present some examples to illustrate the results. Lastly, we use these results to study the class of problems which have uncertainty and inaccuracies in the objective function coefficients of mathematical programming models.

A necessary and sufficient condition for duality in multiobjective variational problems

In this paper we move forward in the study of duality and efficiency in multiobjective variational problems. We introduce new classes of pseudoinvex functions, and prove that not only it is a sufficient condition to establish duality results, but it is also necessary. Moreover, these functions are characterized in order that all Kuhn-Tucker or Fritz John points are efficient solutions. Recent papers are improved. We provide an example to show this improvement and illustrate these classes of functions and results.

Efficient solutions in V-KT-pseudoinvex multiobjective control problems: A characterization

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.

Weak efficiency for multiobjective variational problems

Abstract 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 new class of pseudoinvex functions is equivalent to the class of functions whose weak vector critical points are weakly efficient solution for MVPs.

A necessary and sufficient condition for duality in control problems: KT-invex functionals

In this article, we introduce a new condition on functionals of a control problem, and for that purpose we define the KT-invex functionals. We extend recent optimality control works to the study of duality. In this way we establish weak, strong and converse duality results under KT-invexity. Furthermore, we prove that KT-invexity is not only a sufficient condition for establishing duality, but it is necessary.