Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence

被引:79
作者
Shehu, Yekini [1 ,2 ]
Iyiola, Olaniyi S. [3 ]
机构
[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China
[2] Inst Sci & Technol IST, Campus 1, A-3400 Klosterneuburg, Austria
[3] Calif Univ Penn, Dept Math Comp Sci & Informat Syst, California, PA USA
基金
欧洲研究理事会;
关键词
Alternated inertial; Projection methods; Variational inequality; Pseudo-monotone operator; SUBGRADIENT EXTRAGRADIENT METHOD; CONTRACTION METHODS; GRADIENT METHODS; ALGORITHMS;
D O I
10.1016/j.apnum.2020.06.009
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The projection methods with vanilla inertial extrapolation step for variational inequalities have been of interest to many authors recently due to the improved convergence speed contributed by the presence of inertial extrapolation step. However, it is discovered that these projection methods with inertial steps lose the Fejer monotonicity of the iterates with respect to the solution, which is being enjoyed by their corresponding non-inertial projection methods for variational inequalities. This lack of Fejer monotonicity makes projection methods with vanilla inertial extrapolation step for variational inequalities not to converge faster than their corresponding non-inertial projection methods at times. Also, it has recently been proved that the projection methods with vanilla inertial extrapolation step may provide convergence rates that are worse than the classical projected gradient methods for strongly convex functions. In this paper, we introduce projection methods with alternated inertial extrapolation step for solving variational inequalities. We show that the sequence of iterates generated by our methods converges weakly to a solution of the variational inequality under some appropriate conditions. The Fejer monotonicity of even subsequence is recovered in these methods and linear rate of convergence is obtained. The numerical implementations of our methods compared with some other inertial projection methods show that our method is more efficient and outperforms some of these inertial projection methods. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码:315 / 337
页数:23
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