Stability analysis for set-valued vector mixed variational inequalities in real reflexive Banach spaces
Xing Wang, Nan‐jing Huang · Journal of Industrial and Management Optimization · 2012
In this paper, some characterizations for the solution sets of a class of set-valued vectormixed variational inequalities to be nonempty and bounded arepresented in real reflexive Banach spaces. An equivalence relation betweenthe solution sets of the vector mixed variational inequalities and theweakly efficient solution sets of the vector optimization problems isshown under some suitable assumptions. By using some known results forthe vector optimization problems, several characterizations for thesolution sets of the vector mixed variational inequalities are obtainedin real reflexive Banach spaces. Furthermore, some stability resultsfor the vector mixed variational inequality are given when themapping and the constraint set are perturbed by two different parameters. Finally, the upper semicontinuity and the lower semicontinuity of thesolution sets are given under some suitable assumptions which are different from the ones used in [7, 11, 22]. Some examples are also given to illustrate our results.