A family of three-term conjugate gradient projection methods with a restart procedure and their relaxed-inertial extensions for the constrained nonlinear pseudo-monotone equations with applications - Liu, Pengjie; Shao, Hu; Yuan, Zihang; Wu, Xiaoyu; Zheng, Tianlei (Numerical algorithms, 2023)
Al-Baali et al. ( Comput. Optim. Appl. 60:89–110, 2015) have proposed a three-term conjugate gradient method which satisfies a sufficient descent condition and global convergence. In this paper, we extend this method to a family of three-term conjugate gradient projection methods with a restart procedure and their relaxed-inertial versions for constrained nonlinear pseudo-monotone equations. The accelerated gradient-descent method MSM and the relaxed-inertial strategy are incorporated into the proposed methods to obtain better computational performance. The global convergence of the extended methods are established theoretically without the Lipschitz continuity of the underlying mapping. Numerical results on constrained nonlinear equations show that the extended methods with different settings are efficient. The applicability and efficiency of the extended methods in the regularized decentralized logistic regression and sparse signal restoration problems are also presented and verified.