一种求解单调包含问题的惯性松弛混合邻近外梯度算法

An Inertial Relaxed Hybrid Proximal Extra-Gradient Algorithm for Solving Monotone Inclusions Problems

提出了在希尔伯特空间中求解极大单调包含问题的一种新的惯性松弛混合邻近外梯度算法,考虑到的算法涉及到最近的惯性技术,以及最近提出的混合策略,它将非精确的邻近点与外梯度结合起来.与现有的其它相关算法相比,该算法继承了惯性外推和松弛外梯度策略的良好收敛性.与此同时,还继承了混合邻近外梯度算法的相对误差准则.在适当的参数假设下,通过构造李雅普诺夫函数,从而证明了该算法在适当条件下的收敛性.

In this paper a new inertial relaxed hybrid proximal extragradient algorithm for solving maximal monotone inclusion problems in Hilbert space is studied.Considering that the algorithm involves the recent inertial technique and proposed hybrid strategy,it combines inexact neighbor points with external gradients.Compared with other related algorithms,this algorithm inherits the good convergence of inertia extrapolation and relaxation extra-gradient strategy.At the same time,it also inherits the relative error tolerance of the hybrid proximal extragradient method.Under proper parameter assumptions,the convergence of the algorithm under appropriate conditions by constructing Lyapunov functions is proved.