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A Projection-Proximal Point Algorithm for Solving Generalized Variational Inequalities

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  • Fu-Quan Xia

    (Sichuan Normal University)

  • Nan-Jing Huang

    (Sichuan University)

Abstract

In this paper, a projection-proximal point method for solving a class of generalized variational inequalities is considered in Hilbert spaces. We investigate a general iterative algorithm, which consists of an inexact proximal point step followed by a suitable orthogonal projection onto a hyperplane. We prove the convergence of the algorithm for a pseudomonotone mapping with weakly upper semicontinuity and weakly compact and convex values. We also analyze the convergence rate of the iterative sequence under some suitable conditions.

Suggested Citation

  • Fu-Quan Xia & Nan-Jing Huang, 2011. "A Projection-Proximal Point Algorithm for Solving Generalized Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 150(1), pages 98-117, July.
    • Handle: RePEc:spr:joptap:v:150:y:2011:i:1:d:10.1007_s10957-011-9825-3
    DOI: 10.1007/s10957-011-9825-3
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    References listed on IDEAS

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    1. R. Cominetti, 1997. "Coupling the Proximal Point Algorithm with Approximation Methods," Journal of Optimization Theory and Applications, Springer, vol. 95(3), pages 581-600, December.
    2. R. T. Rockafellar, 1976. "Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 97-116, May.
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    Cited by:

    1. Sorin-Mihai Grad & Felipe Lara, 2021. "Solving Mixed Variational Inequalities Beyond Convexity," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 565-580, August.
    2. Yonghong Yao & Mihai Postolache & Jen-Chih Yao, 2019. "An Iterative Algorithm for Solving Generalized Variational Inequalities and Fixed Points Problems," Mathematics, MDPI, vol. 7(1), pages 1-15, January.
    3. Xin He & Nan-jing Huang & Xue-song Li, 2022. "Modified Projection Methods for Solving Multi-valued Variational Inequality without Monotonicity," Networks and Spatial Economics, Springer, vol. 22(2), pages 361-377, June.
    4. Chinedu Izuchukwu & Yekini Shehu & Chibueze C. Okeke, 2023. "Extension of forward-reflected-backward method to non-convex mixed variational inequalities," Journal of Global Optimization, Springer, vol. 86(1), pages 123-140, May.

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