An explicit hierarchical fixed point algorithm is introduced to solve the monotone variational inequality over the fixed point set of a nonexpansive mapping. This paper discusses a monotone variational inequality with variational constraint and convex optimization problems over the fixed point set of a nonexpansive mapping. The strong convergence for the proposed algorithm to the solution is gu...

In this paper, we introduce and study the system of general variational inequalities which is equivalent to the general variational inequality problem over the product of sets. The usual concept of monotonicity has been extended here. We establish existence results for the solution of general variational inequality problem over the product of sets in the setting of real Hausdroff topological ve...

We consider vector variational inequalities defined by means of the usual componentwise ordering in a finite dimensional Euclidean space. Our principal result shows that, under suitable convexity assumptions, every weak solution of a vector variational inequality is a strong solution of a reduced variational inequality, obtained from the initial one by considering a selection of components.

‎This paper aims at establishing the existence and uniqueness of solutions for a nonstandard variational-hemivariational inequality. The solutions of this inequality are discussed in a subset $K$ of a reflexive Banach space $X$. Firstly, we prove the existence of solutions in the case of bounded closed and convex subsets. Secondly, we also prove the case when $K$ is compact convex subsets. Fina...

Mathematical programs with equilibrium constrains (MPECs) in which the constraints are defined by a parametric variational inequality are considered. Recently, nonlinear programming solvers have been used to solve MPECs. Smoothing algorithms have been very successful. In this note, a smoothing approach based on neural network function to solve MPECs is proposed. The performance of the proposed ...

Abstract We study a nonlinear evolutionary quasi–variational–hemivariational inequality (in short, (QVHVI)) involving set-valued pseudo-monotone map. The central idea of our approach consists introducing parametric variational problem that defines selection associated with (QVHVI). prove the solvability by employing surjectivity theorem for sum operators, combined Minty’s formulation and techni...

Based on the very recent work by Censor-Gibali-Reich [7], we propose an extension of their new variational problem (Split Variational Inequality Problem) to monotone variational inclusions. Relying on the Krasnoselskii-Mann Theorem for averaged operators, we analyze an algorithm for solving a new split monotone inclusions under weaker conditions. Our results improve and develop previously discu...

The paper concerns the study of new classes of parametric optimization problems of the so-called infinite programming that are generally defined on infinite-dimensional spaces of decision variables and contain, among other constraints, infinitely many of inequality constraints. These problems reduce to semi-infinite programs in the case of finite-dimensional spaces of decision variables. We foc...

We use the auxiliary principle technique to suggest and analyze some iterative methods for solving a new class of variational inequalities, which is called the mixed trifunction variational inequality. The mixed trifunction variational inequality includes the trifunction variational inequalities and the classical variational inequalities as special cases. Convergence of these iterative methods ...