Inertial proximal extragradient algorithms for nonsmooth composite optimization
Optimization Eruditorum, Volume 2, Issue 2, August 2025, Pages 97–115
JINTAO YU
School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China
ZHOU WANG
School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China
QUN WANG
School of Data Sciences, Zhejiang University of Finance and Economics, Hangzhou 310018, China
HONGJIN HE
School of Mathematics and Statistics, Ningbo University, Ningbo 315211, China
Abstract
In this paper, we consider a class of nonsmooth composite optimization problems, where the objective is formed as the sum of a differentiable convex function and a simple nonsmooth convex part. By using the inertial technique, we introduce two improved inertial-type extragradient methods for the problem under consideration. The first one is the doubly-inertial proximal extragradient algorithm (DEGA), which employs two inertial steps to generate intermediate iterates for speeding up the performance of the extragradient method. The second algorithm is called overlapped-inertial proximal extragradient algorithm (OEGA), which utilizes the first inertial step to construct a new inertial step so that more historical information could be used in the final update. With appropriate settings on the inertial parameters, our algorithms can recover the benchmark extragradient method. Theoretically, both DEGA and OEGA are globally convergent under some standard assumptions. Moreover, their effectiveness is verified through some numerical experiments on the Dantzig selector and Lasso problems.
Cite this Article as
Jintao Yu, Zhou Wang, Qun Wang and Hongjin He, Inertial proximal extragradient algorithms for nonsmooth composite optimization, Optimization Eruditorum, 2(2), 97–115, 2025