Operations Research Transactions ›› 2021, Vol. 25 ›› Issue (2): 144-148.doi: 10.15960/j.cnki.issn.1007-6093.2021.02.012

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A remark on the convergence of the two-subgradient extragradient algorithm for the variational inequality problem

Biao QU1,*(), Wei XU1, Xinyan WANG1   

  1. 1. Institute of Operations Research, Qufu Normal University, Rizhao 276826, Shandong, China
  • Received:2019-11-19 Online:2021-06-15 Published:2021-05-06
  • Contact: Biao QU E-mail:qubiao001@163.com

Abstract:

The two-subgradient extragradient algorithm was proposed by Yair Censor, Aviv Gibali and Simeon Reich for solving the variational inequality problem. A question about the convergence of this algorithm, that is, whether the sequences generated by the algorithm converge to a solution of the variational inequality problem, was raised as an open problem in the paper "Extensions of Korpelevich's extragradient method for the variational inequality problem in Euclidean space" (Optimization, 61(9): 1119-1132, 2012). Our goal in this short remark is to give an answer to this question and give an integrated proof of the full convergence of the algorithm.

Key words: variational inequality problem, the two-subgradient extragradient algorithm, full convergence

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