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Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems

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  • Bing Tan

    (University of Electronic Science and Technology of China)

  • Xiaolong Qin

    (Hangzhou Normal University)

  • Jen-Chih Yao

    (China Medical University
    National Sun Yat-sen University)

Abstract

This paper investigates some inertial projection and contraction methods for solving pseudomonotone variational inequality problems in real Hilbert spaces. The algorithms use a new non-monotonic step size so that they can work without the prior knowledge of the Lipschitz constant of the operator. Strong convergence theorems of the suggested algorithms are obtained under some suitable conditions. Some numerical experiments in finite- and infinite-dimensional spaces and applications in optimal control problems are implemented to demonstrate the performance of the suggested schemes and we also compare them with several related results.

Suggested Citation

  • Bing Tan & Xiaolong Qin & Jen-Chih Yao, 2022. "Strong convergence of inertial projection and contraction methods for pseudomonotone variational inequalities with applications to optimal control problems," Journal of Global Optimization, Springer, vol. 82(3), pages 523-557, March.
    • Handle: RePEc:spr:jglopt:v:82:y:2022:i:3:d:10.1007_s10898-021-01095-y
    DOI: 10.1007/s10898-021-01095-y
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    References listed on IDEAS

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    6. Yekini Shehu & Aviv Gibali & Simone Sagratella, 2020. "Inertial Projection-Type Methods for Solving Quasi-Variational Inequalities in Real Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 877-894, March.
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    Cited by:

    1. Javad Balooee & Shih-Sen Chang & Lin Wang & Zhaoli Ma, 2022. "Algorithmic Aspect and Convergence Analysis for System of Generalized Multivalued Variational-like Inequalities," Mathematics, MDPI, vol. 10(12), pages 1-40, June.

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