Inertial projection and contraction algorithms with larger step sizes for solving quasimonotone variational inequalities

Zhong-bao Wang (), Xue Chen (), Jiang Yi () and Zhang-you Chen ()
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Zhong-bao Wang: Southwest Jiaotong University
Xue Chen: Southwest Jiaotong University
Jiang Yi: Southwest Jiaotong University
Zhang-you Chen: Southwest Jiaotong University

Journal of Global Optimization, 2022, vol. 82, issue 3, No 4, 499-522

Abstract: Abstract This paper deals with a class of inertial projection and contraction algorithms for solving a variational inequality problem involving quasimonotone and Lipschitz continuous mappings in Hilbert spaces. The algorithms incorporate inertial techniques and the Barzilai–Borwein step size strategy, moreover their line search conditions and some parameters are relaxed to obtain larger step sizes. The weak convergence of the algorithms is proved without the knowledge of the Lipschitz constant of the mappings. Meanwhile, the nonasymptotic convergence and the linear convergence of the algorithms are established. Some numerical experiments show that the proposed algorithms are more effective than some existing ones.

Keywords: Variational inequality; Inertial projection and contraction algorithm; Lipschitz continuity; Quasimonotone mappings; Larger step sizes (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-021-01083-2

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