解絕對值方程式的新平滑函數

Abstract

無中文摘要The system of absolute value equations Ax + B|x| = b, denoted by AVEs, is a non-differentiable NP-hard problem, where A,B are arbitrary given n × n real matrices and b is arbitrary given n-dimensional vector. In this paper, we study four new smoothing functions and propose a smoothing-type algorithm to solve AVEs. With the assumption that the minimal singular value of the matrix A being strictly greater than the maximal singular value of the matrix B, we prove that the algorithm is globally and locally quadratically convergent with the four smooth equations.