Monotonic iterative algorithms for a quasicomplementarity problem (Q2732182)

The quasicomplementarity problem (QCP) for given operators \(A,B:\mathbb{R}^n\to \mathbb{R}^n\) and \(f\in \mathbb{R}^n\) is to find \(u\in \mathbb{R}^n\) such that \(\min\{Au- f,u-Bu\}= 0\). Such problems appear in mathematical programming, they comes often from the discretization of problems in mathematic physics and control theory.NEWLINENEWLINENEWLINEThe authors assume in this paper that is a strictly \(T\)-monotonic operator. Two iterative algorithms for solving QCP are proposed. The first is to solve iteratively a sequence to the case \(Bu=c\), which produces a sequence of approximate solutions convergent monotonically to a solution. The other is a Schwarz algorithm which produces supersolutions converging monotonically to a solution.NEWLINENEWLINENEWLINEThe presented algorithm is the first one of Schwarz type for quasivariational inequalities.