Optimality Conditions in Vector Optimization

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Vector optimization is continuously needed in several science fields, particularly in economy, business, engineering, physics and mathematics. The evolution of these fields depends, in part, on the ...
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Pseudoinvexity: A Good Condition for Efficiency and Weak Efficiency in Multiobjective Mathematical Programming. Characterization.

Pp. 1-16 (16)

DOI: 10.2174/978160805110611001010001

Author(s): M. Arana-Jim´enez, G. Ruiz-Garz´on, A. Rufi´an-Lizana

Abstract

We present new classes of vector invex and pseudoinvex functions which generalize the class of scalar invex functions. These new classes of vector functions are characterized in such a way that every vector critical point is an efficient or a weakly 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, by the introduction of several examples. These results and classes of vector functions are extended to the involved functions in constrained multiobjective mathematical programming problems. It is proved that in order for Kuhn-Tucker points to be efficient or weakly efficient solutions it is necessary and sufficient that the multiobjective problem functions belong to a new class of functions, which we introduce. Similarly, we present characterizations for efficient and weakly efficient solutions by using Fritz John optimality conditions. Some examples are proposed to illustrate these classes of functions and optimality results.

Keywords:

Multiobjective programming, invexity, pseudoinvexity, optimality conditions, efficient solutions.