Inexact Uzawa Algorithms for Variational Inequalities of the Second Kind

An inexact alternating direction method with SQP regularization for the structured variational inequalities

In this paper, we propose an inexact alternating direction method with square quadratic proximal  (SQP) regularization for  the structured variational inequalities. The predictor is obtained via solving SQP system  approximately  under significantly  relaxed accuracy criterion  and the new iterate is computed directly by an explicit formula derived from the original SQP method. Under appropriat...

Efficient Uzawa Algorithms for Two Phase Stefan Type Problems

In this paper we present and analyze Uzawa type algorithms for solving discretized variational inequalities arising from two phase Stefan type problems. For a Uzawa type algorithm and its improved version we show convergence and derive bounds on convergence rates. For the improved Uzawa algorithm, the convergence rate is shown to be uniformly bounded away from 1 if τh−2 is kept bounded, with τ ...

Iterative algorithms for families of variational inequalities fixed points and equilibrium problems

VARIATIONAL ITERATION METHOD FOR FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND

In this paper, He‘s variational iteration method is applied to Fredholm integral equations of the second kind. To illustrate the ability and simplicity of the method, some examples are provided. The results reveal that the proposed method is very effective and simple and for first fourth examples leads to the exact solution.

Two new variants of nonlinear inexact Uzawa algorithms for saddle-point problems

In this paper, we consider some nonlinear inexact Uzawa methods for iteratively solving linear saddle-point problems. By means of a new technique, we first give an essential improvement on the convergence results of Bramble-Paschiak-Vassilev for a known nonlinear inexact Uzawa algorithm. Then we propose two new algorithms, which can be viewed as a combination of the known nonlinear inexact Uzaw...