A system of nonlinear set valued variational inclusions

Abstract

In this paper, we studied the existence theorems and techniques for finding the solutions of a system of nonlinear set valued variational inclusions in Hilbert spaces. To overcome the difficulties, due to the presence of a proper convex lower semicontinuous function ϕ and a mapping g which appeared in the considered problems, we have used the resolvent operator technique to suggest an iterative algorithm to compute approximate solutions of the system of nonlinear set valued variational inclusions. The convergence of the iterative sequences generated by algorithm is also proved.AMS Mathematics subject classification49J40; 47H06

An Iterative Algorithm for the Nonlinear MC2 Model with Variational Inequality Method

“…Mathematical conditions, including a constraint qualification and convexity of the feasible set were shown by Toyasaki et al [23], which allowed for characterizing the economic problem by using a variational inequality formulation. An iterative algorithm was suggested by the resolvent operator technique to compute approximate solutions of the system of nonlinear set valued variational inclusion [24]. The affine variational inequality problems and the polynomial complementary problems were discussed in [25]; here, it is the extension of the results in [24].…”

“…An iterative algorithm was suggested by the resolvent operator technique to compute approximate solutions of the system of nonlinear set valued variational inclusion [24]. The affine variational inequality problems and the polynomial complementary problems were discussed in [25]; here, it is the extension of the results in [24]. Then, the authors applied their results to discuss the existence of the solutions of weakly homogeneous nonlinear equations, the domains of which are closed convex cones.…”

Relaxed resolvent operator for solving a variational inclusion problem

“…The theory of variational inequalities was initially developed to deal with equilibrium problems, precisely the Signorini problem. After that it has been extended and generalized to study a wide class of problems arising in mechanics, physics, optimization and control, nonlinear programming, economics, finance, regional structural,transformation, elasticity, and applied sciences, etc., see e.g., [1,2,4,12,15,16,17,18,19,20] and references therein.…”