A globally and quadratically convergent method for absolute value equations

作者：Caccetta Louis; Qu Biao; Zhou Guanglu^*

来源：Computational Optimization and Applications, 2011, 48(1): 45-58.

DOI：10.1007/s10589-009-9242-9

• Absolute value equations
• Smoothing Newton method
• Global convergence
• Convergence rate

We investigate the NP-hard absolute value equation (AVE) Ax - vertical bar x vertical bar = b, where A is an arbitrary n x n real matrix. In this paper, we propose a smoothing Newton method for the AVE. When the singular values of A exceed 1, we show that this proposed method is globally convergent and the convergence rate is quadratic. Preliminary numerical results show that this method is promising.

• 出版日期2011-1
• 单位曲阜师范大学