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Operations Research Transactions >

2023 , Vol. 27 >Issue 1: 127 - 137

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2023.01.009

A new projection and contraction algorithm for solving quasimonotone variational inequalities

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  • 1. Sichuan Colleges and Universities Key Laboratory of Optimization Theory and Applications, School of Mathematics and Information, China West Normal University, Nanchong, 637009, Sichuan, China

Received date: 2022-09-28

  Online published: 2023-03-16

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Abstract

In 2020, Liu and Yang proposed a projection algorithm (LYA for short) for solving quasi-monotone and Lipschitz continuous variational inequalities problem (VIP for short) in Hilbert space. In this paper, we present a new projection and contraction algorithm (NPCA for short) for solving quasi-monotone VIP in Euclidean space. The new algorithm weakens the Lipschitz continuity of the underlying mapping in LYA. NPCA clusters to the solution of VIP whenever the underlying mapping is continuous, quasi-monotone and the solution set of dual variational inequality is nonempty. The global convergence of NPCA needs an additional assumption about the solution set of VIP. Numerical experiments show that NPCA is more efficient than LYA from the total number of iterative point of view, and the CPU time point of view in high dimensional quasi-monotone VIP.

Key words： variational inequalities; quasi-monotone; projection and contraction algorithm; continuity

Cite this article

Minglu YE, Huan DENG . A new projection and contraction algorithm for solving quasimonotone variational inequalities[J]. Operations Research Transactions, 2023 , 27(1) : 127 -137 . DOI: 10.15960/j.cnki.issn.1007-6093.2023.01.009

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