Schwarz Method for Variational Inequalities Related to Ergodic Control Problems

A Relaxed Extra Gradient Approximation Method of Two Inverse-Strongly Monotone Mappings for a General System of Variational Inequalities, Fixed Point and Equilibrium Problems

An additive Schwarz method for variational inequalities

This paper proposes an additive Schwarz method for variational inequalities and their approximations by finite element methods. The Schwarz domain decomposition method is proved to converge with a geometric rate depending on the decomposition of the domain. The result is based on an abstract framework of convergence analysis established for general variational inequalities in Hilbert spaces.

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 ...

Convergence Rate Analysis of a Multiplicative Schwarz Method for Variational Inequalities

This paper derives a linear convergence for the Schwarz overlapping domain decomposition method when applied to constrained minimization problems. The convergence analysis is based on a minimization approach to the corresponding functional over a convex set. A general framework of convergence is established for some multiplicative Schwarz algorithm. The abstract theory is particularly applied t...

Ergodicity of Robust Switching Control and Nonlinear System of Quasi-Variational Inequalities

We analyze the asymptotic behavior for a system of fully nonlinear parabolic and elliptic quasi variational inequalities. These equations are related to robust switching control problems introduced in [6]. We prove that, as time horizon goes to infinity (resp. discount factor goes to zero) the long run average solution to the parabolic system (resp. the limiting discounted solution to the ellip...