A SMOOTHING-TYPE ALGORITHM FOR ABSOLUTE VALUE EQUATIONS

作者：Jiang Xiaoqin; Zhang Ying^*

来源：Journal of Industrial and Management Optimization, 2013, 9(4): 789-798.

DOI：10.3934/jimo.2013.9.789

• Absolute value equations
• uniquely solvable
• smoothing-type algorithm
• global convergence
• local quadratic convergence

The system of absolute value equations Ax + B vertical bar x vertical bar = b , denoted by AVEs, is proved to be NP-hard, where A, B are arbitrary given n x n real matrices and b is arbitrary given n-dimensional vector. In this paper, we reformulate AVEs as a family of parameterized smooth equations and propose a smoothing-type algorithm to solve AVEs. Under the assumption that the minimal singular value of the matrix A is strictly greater than the maximal singular value of the matrix B, we prove that the algorithm is well-defined. In particular, we show that the algorithm is globally convergent and the convergence rate is quadratic without any additional assumption. The preliminary numerical results are reported, which show the effectiveness of the algorithm.

• 出版日期2013-10
• 单位天津大学