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

Author

Listed:
  • Zhong-bao Wang

    (Southwest Jiaotong University
    National Engineering Laboratory of Integrated Transportation Big Data Application Technology
    University of Electronic Science and Technology of China)

  • Xue Chen

    (Southwest Jiaotong University)

  • Jiang Yi

    (Southwest Jiaotong University
    National Engineering Laboratory of Integrated Transportation Big Data Application Technology)

  • Zhang-you Chen

    (Southwest Jiaotong University
    National Engineering Laboratory of Integrated Transportation Big Data Application Technology)

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.

Suggested Citation

  • Zhong-bao Wang & Xue Chen & Jiang Yi & Zhang-you Chen, 2022. "Inertial projection and contraction algorithms with larger step sizes for solving quasimonotone variational inequalities," Journal of Global Optimization, Springer, vol. 82(3), pages 499-522, March.
    • Handle: RePEc:spr:jglopt:v:82:y:2022:i:3:d:10.1007_s10898-021-01083-2
    DOI: 10.1007/s10898-021-01083-2
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    References listed on IDEAS

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    1. Xingju Cai & Guoyong Gu & Bingsheng He, 2014. "On the O(1/t) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators," Computational Optimization and Applications, Springer, vol. 57(2), pages 339-363, March.
    2. Q. L. Dong & Y. J. Cho & L. L. Zhong & Th. M. Rassias, 2018. "Inertial projection and contraction algorithms for variational inequalities," Journal of Global Optimization, Springer, vol. 70(3), pages 687-704, March.
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