A Penalty Approach for Solving Generalized Absolute Value Equations

Abstract

In this paper, we propose a penalty approach for solving generalized absolute value equations (GAVEs) of the type Ax−B|x|=b, (A,B∈Rn×n,b∈Rn). Firstly, we reformulate the GAVEs as variational inequality problems passing through an equivalent horizontal linear complementarity problem. To approximate the resulting variational inequality, a sequence of nonlinear equations containing a penalty term is then defined. Under a mild assumption, we show that the solution of the considered sequence converges to that of GAVE if the penalty parameter tends to infinity. An algorithm is developed where its corresponding theoretical arguments are well established. Finally, some numerical experiments are presented to show that our approach is quite appreciable.