伪单调变分不等式的一种大步长自适应次梯度外梯度投影算法

Alarge step adaptive sub-gradient and exter-gradient projection algorithm for pseudomonotone variational inequalities

2020年Pham Ky Anh等人在Hilbert空间中提出了一种求解映射伪单调且Lipschitz连续的自适应投影算法(简记为PDNA).该算法无需知道映射的Lipschitz系数,且具有强收敛的结果.注意到算法的步长与其收敛速度密切相关,通常大步长的算法具有更好的收敛速度.Liu和Yang提出了一种求解拟单调变分不等式的自适应算法(简记为LYA),LYA的步长比PDNA中的步长长.本文提出了一种自适应的求解映射伪单调且Lipschitz连续的次梯度外梯度投影算法.新算法的步长比LYA长,且可以退化为LYA中的步长.在与PDNA相同的假设条件下证明了新算法的强收敛性.数值实验表明新算法有更好的数值实验结果.

In 2020,Pham Ky Anh et al.proposed an adaptive projection algorithm(abbreviated as PDNA)in Hilbert space for solving the mapping pseudo-monotone and Lipschitz continuous.The algorithm does not need to know the Lipschitz coefficient of the map,and has a strong convergence result.It is noted that the step size of the algorithm is closely related to its convergence speed,and generally the algorithm with long strides has better convergence speed.Liu and Yang propose an adaptive algorithm for solving quasi-monotone variational inequalities(abbreviated LYA)with a step size longer than the step size in PDNA.In this paper,we propose an adaptive subgradient external gradient projection algorithm for solving the mapping pseudo-monotone and Lipschitz continuous.The step size of the new algorithm is longer than that of LYA and can be degraded to the step size of LYA.The strong convergence of the new algorithm is proved under the same assumptions as that of PDNA.Numerical experiments show that the new algorithm has better numerical experimental results.