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Strong Convergent Inertial Two-subgradient Extragradient Method for Finding Minimum-norm Solutions of Variational Inequality Problems

Author

Listed:
  • Timilehin Opeyemi Alakoya

    (University of KwaZulu-Natal)

  • Oluwatosin Temitope Mewomo

    (University of KwaZulu-Natal)

Abstract

In 2012, Censor et al. (Extensions of Korpelevich’s extragradient method for the variational inequality problem in Euclidean space. Optimization 61(9):1119–1132, 2012b) proposed the two-subgradient extragradient method (TSEGM). This method does not require computing projection onto the feasible (closed and convex) set, but rather the two projections are made onto some half-space. However, the convergence of the TSEGM was puzzling and hence posted as open question. Very recently, some authors were able to provide a partial answer to the open question by establishing weak convergence result for the TSEGM though under some stringent conditions. In this paper, we propose and study an inertial two-subgradient extragradient method (ITSEGM) for solving monotone variational inequality problems (VIPs). Under more relaxed conditions than the existing results in the literature, we prove that proposed method converges strongly to a minimum-norm solution of monotone VIPs in Hilbert spaces. Unlike several of the existing methods in the literature for solving VIPs, our method does not require any linesearch technique, which could be time-consuming to implement. Rather, we employ a simple but very efficient self-adaptive step size method that generates a non-monotonic sequence of step sizes. Moreover, we present several numerical experiments to demonstrate the efficiency of our proposed method in comparison with related results in the literature. Finally, we apply our result to image restoration problem. Our result in this paper improves and generalizes several of the existing results in the literature in this direction.

Suggested Citation

  • Timilehin Opeyemi Alakoya & Oluwatosin Temitope Mewomo, 2024. "Strong Convergent Inertial Two-subgradient Extragradient Method for Finding Minimum-norm Solutions of Variational Inequality Problems," Networks and Spatial Economics, Springer, vol. 24(2), pages 425-459, June.
    • Handle: RePEc:kap:netspa:v:24:y:2024:i:2:d:10.1007_s11067-024-09615-5
    DOI: 10.1007/s11067-024-09615-5
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    References listed on IDEAS

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    1. Heinz H. Bauschke & Patrick L. Combettes, 2001. "A Weak-to-Strong Convergence Principle for Fejér-Monotone Methods in Hilbert Spaces," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 248-264, May.
    2. Stella Dafermos, 1980. "Traffic Equilibrium and Variational Inequalities," Transportation Science, INFORMS, vol. 14(1), pages 42-54, February.
    3. Smith, M. J., 1979. "The existence, uniqueness and stability of traffic equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 13(4), pages 295-304, December.
    4. Ciarcià, Carla & Daniele, Patrizia, 2016. "New existence theorems for quasi-variational inequalities and applications to financial models," European Journal of Operational Research, Elsevier, vol. 251(1), pages 288-299.
    5. 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.
    6. Laura Scrimali & Cristina Mirabella, 2018. "Cooperation in pollution control problems via evolutionary variational inequalities," Journal of Global Optimization, Springer, vol. 70(2), pages 455-476, February.
    7. Y. Censor & A. Gibali & S. Reich, 2011. "The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 318-335, February.
    8. Suthep Suantai & Pronpat Peeyada & Damrongsak Yambangwai & Watcharaporn Cholamjiak, 2020. "A Parallel-Viscosity-Type Subgradient Extragradient-Line Method for Finding the Common Solution of Variational Inequality Problems Applied to Image Restoration Problems," Mathematics, MDPI, vol. 8(2), pages 1-31, February.
    9. Anna Nagurney & David Parkes & Patrizia Daniele, 2007. "The Internet, evolutionary variational inequalities, and the time-dependent Braess paradox," Computational Management Science, Springer, vol. 4(4), pages 355-375, October.
    10. Lawphongpanich, Siriphong & Hearn, Donald W., 1984. "Simplical decomposition of the asymmetric traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 18(2), pages 123-133, April.
    11. Timilehin O. Alakoya & Oluwatosin T. Mewomo & Yekini Shehu, 2022. "Strong convergence results for quasimonotone variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(2), pages 249-279, April.
    12. Songnian He & Hong-Kun Xu, 2013. "Uniqueness of supporting hyperplanes and an alternative to solutions of variational inequalities," Journal of Global Optimization, Springer, vol. 57(4), pages 1375-1384, December.
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