Internal and subspace correction approximations of implicit variational inequalities

Approximation results and subspace correction algorithms for implicit variational inequalities

Strong convergence for variational inequalities and equilibrium problems and representations

We introduce an implicit method for nding a common element of the set of solutions of systems of equilibrium problems and the set of common xed points of a sequence of nonexpansive mappings and a representation of nonexpansive mappings. Then we prove the strong convergence of the proposed implicit schemes to the unique solution of a variational inequality, which is the optimality condition for ...

Projection Iterative Approximations for a New Class of General Random Implicit Quasi-variational Inequalities

We introduce a class of projection-contraction methods for solving a class of general random implicit quasi-variational inequalities with random multivalued mappings in Hilbert spaces, construct some random iterative algorithms, and give some existence theorems of random solutions for this class of general random implicit quasi-variational inequalities. We also discuss the convergence and stabi...

Fast solution of Cahn-Hilliard variational inequalities using implicit time discretization and finite elements

We consider the efficient solution of the Cahn-Hilliard variational inequality using an implicit time discretization, which is formulated as an optimal control problem with pointwise constraints on the control. By applying a semi-smooth Newton method combined with a Moreau-Yosida regularization technique for handling the control constraints we show superlinear convergence in function space. At ...

Vector Optimization Problems and Generalized Vector Variational-Like Inequalities

In this paper, some properties of  pseudoinvex functions, defined by means of  limiting subdifferential, are discussed. Furthermore, the Minty vector variational-like inequality,  the Stampacchia vector variational-like inequality, and the  weak formulations of these two inequalities  defined by means of limiting subdifferential are studied. Moreover, some relationships  between the vector vari...