Convergence Analysis of Projection Method for Variational Inequalities

Abstract

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.

arXiv comment24 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:2101.08057

References in corpus (5)

• An inertial forward-backward algorithm for monotone inclusions
• Projected Reflected Gradient Methods for Monotone Variational Inequalities
• The rate of convergence of Nesterov's accelerated forward-backward method is actually faster than $1/k^2$
• A hybrid method without extrapolation step for solving variational inequality problems
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Cited by in corpus (3)

• Self adaptive inertial extragradient algorithms for solving variational inequality problems
• Weak Convergence for Variational Inequalities with Inertial-Type Method
• Strong convergence of inertial extragradient algorithms for solving variational inequalities and fixed point problems