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New inertial forward-backward type for variational inequalities with Quasi-monotonicity

Author

Listed:
  • Chinedu Izuchukwu

    (The Technion–Israel Institute of Technology)

  • Yekini Shehu

    (Zhejiang Normal University)

  • Jen-Chih Yao

    (China Medical University)

Abstract

In this paper, we present a modification of the forward-backward splitting method with inertial extrapolation step and self-adaptive step sizes to solve variational inequalities in a quasi-monotone setting. Our proposed method involves one computation of the projection onto the feasible set and one evaluation of the operator per iteration, which is simpler than most methods available in the literature to solve similar problems. We first establish weak convergence result when the set of solutions of the Minty formulation of the variational inequality is nonempty in infinite dimensional Hilbert spaces under appropriate conditions. Next, we give linear convergence result when the operator is strongly pseudo-monotone. We also give numerical implementations of our proposed method and some comparisons with some other methods available in the literature.

Suggested Citation

  • Chinedu Izuchukwu & Yekini Shehu & Jen-Chih Yao, 2022. "New inertial forward-backward type for variational inequalities with Quasi-monotonicity," Journal of Global Optimization, Springer, vol. 84(2), pages 441-464, October.
    • Handle: RePEc:spr:jglopt:v:84:y:2022:i:2:d:10.1007_s10898-022-01152-0
    DOI: 10.1007/s10898-022-01152-0
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    References listed on IDEAS

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