Abstract
In this paper, we introduce the concept of a second-order composed contingent epiderivative for set-valued maps and discuss some of its properties. Then, by virtue of the second-order composed contingent epiderivative, we establish second-order sufficient optimality conditions and necessary optimality conditions for the weakly efficient solution of set-valued vector equilibrium problems with unconstraints and set-valued vector equilibrium problems with constraints, respectively. MSC:90C46, 91B50.
Highlights
The vector equilibrium problem, which contains vector optimization problems, vector variational inequality problems and vector complementarity problems as special case, has been studied
Giannessi et al [ ] turned the vector variational inequalities with constraints into another vector variational inequalities without constraints. They gave the sufficient conditions for the efficient solution and the weakly efficient solution of the vector variational inequalities in finite dimensional spaces
Motivated by the work reported in [, ], we introduce a new secondorder derivative called second-order composed contingent epiderivative for set-valued maps and obtain some of its properties
Summary
The vector equilibrium problem, which contains vector optimization problems, vector variational inequality problems and vector complementarity problems as special case, has been studied (see [ – ]). By virtue of the second-order composed contingent epiderivative, we obtain second-order sufficient optimality conditions and necessary optimality conditions for the weakly efficient solution of set-valued vector equilibrium problems.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
