Pseudoinvexity: A Good Condition for Efficiency and Weak Efficiency in Multiobjective Mathematical Programming. Characterization.
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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.
Multiobjective programming, invexity, pseudoinvexity, optimality conditions,