求解一类特殊极大值函数方程的光滑谱共轭梯度法

Smoothing Spectral Conjugate Gradient Method for Solving a Class of Special Max-type Functions Equations

考虑了一类含有绝对值函数的特殊极大值函数非光滑方程问题的求解方法,基于极大值函数与绝对值函数的光滑函数,给出了求解此类非光滑方程的光滑谱共轭梯度法.在一般的假设条件下,证明了方法的全局收敛性,并且相关的数值实验表明了方法的有效性.

A method for solving nonsmooth equations with absolute-value function with a special class of max-type functions was considered. Based on the smooth function of the max-type functions and the absolute-value function, a smoothing spectral conjugate gradient method for solving such nonsmooth equations was given. The global convergence of the method was proved, and the effectiveness of the given method was shown by the related numerical experiments.