4,224 research outputs found
Duality for multiobjective variational control problems with (Φ,ρ)-invexity
In this paper, Mond-Weir and Wolfe type duals for multiobjective variational control problems are formulated. Several duality theorems are established relating efficient solutions of the primal and dual multiobjective variational control problems under TeX-invexity. The results generalize a number of duality results previously established for multiobjective variational control problems under other generalized convexity assumptions
Sufficient optimality criteria and duality for multiobjective variational control problems with G-type I objective and constraint functions
In the paper, we introduce the concepts of G-type I and generalized G-type I
functions for a new class of nonconvex multiobjective variational control problems. For
such nonconvex vector optimization problems, we prove sufficient optimality conditions for
weakly efficiency, efficiency and properly efficiency under assumptions that the functions
constituting them are G-type I and/or generalized G-type I objective and constraint functions.
Further, for the considered multiobjective variational control problem, its dual multiobjective
variational control problem is given and several duality results are established under
(generalized) G-type I objective and constraint functions
Weak Minimizers, Minimizers and Variational Inequalities for set valued Functions. A blooming wreath?
In the literature, necessary and sufficient conditions in terms of
variational inequalities are introduced to characterize minimizers of convex
set valued functions with values in a conlinear space. Similar results are
proved for a weaker concept of minimizers and weaker variational inequalities.
The implications are proved using scalarization techniques that eventually
provide original problems, not fully equivalent to the set-valued counterparts.
Therefore, we try, in the course of this note, to close the network among the
various notions proposed. More specifically, we prove that a minimizer is
always a weak minimizer, and a solution to the stronger variational inequality
always also a solution to the weak variational inequality of the same type. As
a special case we obtain a complete characterization of efficiency and weak
efficiency in vector optimization by set-valued variational inequalities and
their scalarizations. Indeed this might eventually prove the usefulness of the
set-optimization approach to renew the study of vector optimization
Variational inequalities characterizing weak minimality in set optimization
We introduce the notion of weak minimizer in set optimization. Necessary and
sufficient conditions in terms of scalarized variational inequalities of
Stampacchia and Minty type, respectively, are proved. As an application, we
obtain necessary and sufficient optimality conditions for weak efficiency of
vector optimization in infinite dimensional spaces. A Minty variational
principle in this framework is proved as a corollary of our main result.Comment: Includes an appendix summarizing results which are submitted but not
published at this poin
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