解绝对值方程的广义信赖域算法

A generalized trust region algorithm for absolute value equations

绝对值方程是一个不可微的NP-hard问题。基于︱x︱次梯度的广义Jacobian矩阵,提出了广义的信赖域算法。证明了该算法是适定的,同时在一定的条件下具有全局收敛性。数值实验表明该算法对于求解绝对值方程问题(最大维数达到2 000)是有效的。

Absolute value equations is a non-differentiable NP-hard problem. In this paper,a trust region algorithm with generalized Jacobian matrix of ｜ x ｜ based on a subgradient is proposed. Under mild conditions,the well-definedness and global convergence of the presented algorithm are proved.The numerical results indicate that the proposed algorithm is very effective for solving absolute value equations（ with a maximum dimension of 2 000）.