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Publication Details
AFRICAN RESEARCH NEXUS
SHINING A SPOTLIGHT ON AFRICAN RESEARCH
mathematics
Projection methods with alternating inertial steps for variational inequalities: Weak and linear convergence
Applied Numerical Mathematics, Volume 157, Year 2020
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Description
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 Fejér 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 Fejér 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 Fejér 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. © 2020 IMACS
Authors & Co-Authors
Shehu, Yekini
China, Jinhua
Zhejiang Normal University
Austria, Klosterneuburg
Institute of Science and Technology Austria Ista
Iyiola, Olaniyi S.
United States, California
California University of Pennsylvania
Statistics
Citations: 68
Authors: 2
Affiliations: 3
Identifiers
Doi:
10.1016/j.apnum.2020.06.009
ISSN:
01689274