A modified augmented Lagrangian method for a class of monotone variational inequalities

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

Solutions of variational inequalities on fixed points of nonexpansive mappings

n this paper , we propose a generalized iterative method forfinding a common element of the set of fixed points of a singlenonexpannsive mapping and the set of solutions of two variationalinequalities with inverse strongly monotone mappings and strictlypseudo-contractive of Browder-Petryshyn type mapping. Our resultsimprove and extend the results announced by many others.

An inexact parallel splitting augmented Lagrangian method for large system of linear equations

Parallel iterative methods are powerful tool for solving large system of linear equations (LEs). The existing parallel computing research results are focussed mainly on sparse system or others with particular structure. And most are based on parallel implementation of the classical relaxation methods such as Gauss-Seidel, SOR, and AOR methods carried efficiently on multiprcessor systems. In thi...

Smooth methods of multipliers for complementarity problems

This paper describes several methods for solving nonlinear complementarity problems. A general duality framework for pairs of monotone operators is developed and then applied to the monotone complementarity problem, obtaining primal, dual, and primal-dual formulations. We derive Bregman-function-based generalized proximal algorithms for each of these formulations, generating three classes of co...

Augmented Lagrangian method for solving absolute value equation and its application in two-point boundary value problems

One of the most important topic that consider in recent years by researcher is absolute value equation (AVE). The absolute value equation seems to be a useful tool in optimization since it subsumes the linear complementarity problem and thus also linear programming and convex quadratic programming. This paper introduce a new method for solving absolute value equation. To do this, we transform a...