Duality for Vector Optimization of Set-Valued Functions

Existence and Lagrangian Duality .for Maximizations of Set-Valued Functions

The maximization with respect to a cone of a set-valued function into possibly infinite dimensions is defined; some existence results are established; and a Lagrangian duality theory is developed.

Approximate Fenchel-Lagrangian Duality for Constrained Set-Valued Optimization Problems

In this article, we construct a Fenchel-Lagrangian ε-dual problem for set-valued optimization problems by using the perturbation methods. Some relationships between the solutions of the primal and the dual problems are discussed. Moreover, an ε-saddle point theorem is proved.

Lower semicontinuity for parametric set-valued vector equilibrium-like problems

A concept of weak $f$-property for a set-valued mapping is introduced‎, ‎and then under some suitable assumptions‎, ‎which do not involve any information‎ ‎about the solution set‎, ‎the lower semicontinuity of the solution mapping to‎ ‎the parametric‎ ‎set-valued vector equilibrium-like problems are derived by using a density result and scalarization method‎, ‎where the‎ ‎constraint set $K$...

Optimality Conditions for Vector Optimization with Set-Valued Maps

In this paper, we establish a Farkas-Minkowski type alternative theorem under the supposition of nearly semiconvexlike set-valued maps. Based on the alternative theorem and some other lemmas, we present necessary optimality conditions and sufficient optimality conditions for set-valued vector optimization problems with extended inequality constraints in a sense of weak E-minimizers.

K-epiderivatives for set-valued functions and optimization