Convergence analysis of projection method for variational inequalities - Shehu, Yekini; Iyiola, Olaniyi S.; Li, Xiao-Huan; Dong, Qiao-Li; Discrete Optimization in Computer Vision: Theory and Practice (Computational and Applied Mathematics, 2019)
The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is monotone and uniformly continuous. We carry out a unified analysis of the proposed method under very mild assumptions. In particular, weak convergence of the generated sequence is established and nonasymptotic O(1 / n) rate of convergence is established, where n denotes the iteration counter. We also present some experimental results to illustrate the profits gained by introducing the inertial extrapolation steps.
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