In this paper, we introduce a new system of quasi variational inequalities. The projection technique is used to establish the equivalence between this new system of quasi variational inequalities and the fixed point problem. The fixed point formulation enables us to suggest some parallel projection iterative methods for solving the system of quasi variational inequalities. Convergence analysis ...

In this paper, we suggest and consider a class of new three-step approximation schemes for generalized general set-valued mixed quasi variational inequalities. We also consider and analyze a new class of extragradienttype methods for solving generalized set-valued variational inequalities. The proposed methods include several new and known methods as special cases. Our results present a signifi...

In this paper, we consider a new system of quasi variational inequalities involving two different operators. Using the projection technique, we suggest and analyze a new iterative method for solving this system of quasi variational inequalities. We also prove the convergence of this iterative method under some mild conditions. As a special case, our results include the results of Huang and Noor...

In this communication, we establish some existence theorem for a new class of generalized mixed vector quasi-variationallike inequalities with fuzzy mappings in topological vector spaces by using the KKM-Fan Theorem and an equivalent fixed point theorem.

In this paper we consider a elastic vector-valued Allen-Cahn MPCC (Mathematical Programs with Complementarity Constraints) problem. We use a regularization approach to get the optimality system for the subproblems. By passing to the limit in the optimality conditions for the regularized subproblems, we derive certain generalized first-order necessary optimality conditions for the original problem.

In this paper, we consider mixed vector variational-like inequality problems in the setting of topological vector spaces. We extend the concept of upper sign continuity for vector-valued mappings. Further, by exploiting KKM-Fan lemma, we establish some existence results for solutions of mixed vector variational-like inequality problems and show that the solution sets of these problems are compact.

The majority of First Order methods for large-scale convex-concave saddle point problems and variational inequalities with monotone operators are proximal algorithms which at every iteration need to minimize over problem’s domain X the sum of a linear form and a strongly convex function. To make such an algorithm practical, X should be proximal-friendly – admit a strongly convex function with e...