The connectedness of the solutions set for set-valued vector equilibrium problems under improvement sets

In this paper, we provide the connectedness of the sets of weak efficient solutions, Henig efficient solutions and Benson proper efficient solutions for set-valued vector equilibrium problems under improvement sets.

New second-order radial epiderivatives and applications to optimality conditions

In this paper, we introduce the second-order weakly composed radial epiderivative of set-valued maps, discuss its relationship to the second-order weakly composed contingent epiderivative, and obtain some of its properties. Then we establish the necessary optimality conditions and sufficient optimality conditions of Benson proper efficient solutions of constrained set-valued optimization problems by means of the second-order epiderivative. Some of our results improve and imply the corresponding ones in recent literature.

On connectedness of the set of efficient solutions for generalized systems

In this paper, we first give a density theorem. We will see that, under some suitable conditions, the set of positive proper efficient solutions is dense in the set of the efficient solutions. Finally, we discuss about the connectedness for the set of the efficient solutions of a generalized system.

Second-Order Optimality Conditions for Set-Valued Optimization Problems Under Benson Proper Efficiency

Some new properties are obtained for generalized second-order contingent (adjacent) epiderivatives of set-valued maps. By employing the generalized second-order adjacent epiderivatives, necessary and sufficient conditions of Benson proper efficient solutions are given for set-valued optimization problems. The results obtained improve the corresponding results in the literature.