A modified multivariate spectral gradient algorithm for solving absolute value equations

Abstract In this paper, a modified multivariate spectral gradient algorithm is proposed for solving the absolute value equations  A x − | x | = b , where  A ∈ R n × n , b ∈ R n and  x ∈ R n . Some properties of the absolute value equations are analyzed, and the global convergence of the proposed algorithm based on some appropriate assumptions is discussed. Several examples are given to illustrate the effectiveness and competitiveness of our algorithm.