Weak convergence of iterative methods for solving quasimonotone variational inequalities

Hongwei Liu () and Jun Yang ()
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Hongwei Liu: Xidian University
Jun Yang: Xidian University

Computational Optimization and Applications, 2020, vol. 77, issue 2, No 7, 508 pages

Abstract: Abstract In this work, we introduce self-adaptive methods for solving variational inequalities with Lipschitz continuous and quasimonotone mapping(or Lipschitz continuous mapping without monotonicity) in real Hilbert space. Under suitable assumptions, the convergence of algorithms are established without the knowledge of the Lipschitz constant of the mapping. The results obtained in this paper extend some recent results in the literature. Some preliminary numerical experiments and comparisons are reported.

Keywords: Variational inequalities; Projection; Gradient method; Quasimonotone mapping; Convex set; 47J20; 90C25; 90C30; 90C52 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s10589-020-00217-8

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