求解绝对值方程的多元谱梯度投影方法

MULTIVARIATE SPECTRAL GRADIENT PROJECTION METHOD FOR SOLVING ABSOLUTE VALUE EQUATION

受多元谱梯度投影算法(MMSGP)的启发,对该方法进行改进,用于求解绝对值方程(AVE),在梯度差中加入松弛因子,y_(k-1)=λ(F_(k)-F_(k-1))+(2-λ)rs_(k-1)并引用一种新的线搜索策略,从而实现减少迭代次数和加快收敛速度的效果,并证明了该算法在适当的假设条件下是全局收敛的。数值实验表明,改进后的算法是可行的和有效的。

Inspired by the multivariate spectral gradient projection algorithm(MMSGP),the method is improved to solve the absolute value equation(AVE),and the relaxation factor is added to the gradient difference y_(k-1)=λ(F_(k)-F_(k-1))+(2-λ)rs_(k-1) and a new line search strategy is quoted to reduce the number of iterations and speed up the convergence speed,and it proves that the algorithm is globally convergent under appropriate assumptions.Numerical experiments show that the improved algorithm is feasible and effective.