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Weak convergence of iterative methods for solving quasimonotone variational inequalities

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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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xidian University, Xi’an, 710126, Shaanxi, China

    Hongwei Liu & Jun Yang

  2. School of Mathematics and Information Science, Xianyang Normal University, Xianyang, 712000, Shaanxi, China

    Jun Yang

Authors
  1. Hongwei Liu
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  2. Jun Yang
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Correspondence to Jun Yang.

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Liu, H., Yang, J. Weak convergence of iterative methods for solving quasimonotone variational inequalities. Comput Optim Appl 77, 491–508 (2020). https://doi.org/10.1007/s10589-020-00217-8

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