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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. B. S. He & L. Z. Liao, 2002. "Improvements of Some Projection Methods for Monotone Nonlinear Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 111-128, January.
    2. Jun Yang & Hongwei Liu, 2020. "A self-adaptive method for pseudomonotone equilibrium problems and variational inequalities," Computational Optimization and Applications, Springer, vol. 75(2), pages 423-440, March.
    3. Minglu Ye & Yiran He, 2015. "A double projection method for solving variational inequalities without monotonicity," Computational Optimization and Applications, Springer, vol. 60(1), pages 141-150, January.
    4. 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.
    5. W. Liu & Y. H. Dai, 2001. "Minimization Algorithms Based on Supervisor and Searcher Cooperation," Journal of Optimization Theory and Applications, Springer, vol. 111(2), pages 359-379, November.
    6. Jamilu Abubakar & Poom Kumam & Habib ur Rehman & Abdulkarim Hassan Ibrahim, 2020. "Inertial Iterative Schemes with Variable Step Sizes for Variational Inequality Problem Involving Pseudomonotone Operator," Mathematics, MDPI, vol. 8(4), pages 1-25, April.
    7. Hongwei Liu & Jun Yang, 2020. "Weak convergence of iterative methods for solving quasimonotone variational inequalities," Computational Optimization and Applications, Springer, vol. 77(2), pages 491-508, November.
    8. 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.
    9. Dang Van Hieu & Jean Jacques Strodiot & Le Dung Muu, 2020. "An Explicit Extragradient Algorithm for Solving Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 476-503, May.
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