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Strongly Convergent Golden Ratio Algorithms for Variational Inequalities

Author

Listed:
  • Yonghong Yao

    (Tiangong University
    China Medical University Hospital, China Medical University
    Kyung Hee University)

  • Abubakar Adamu

    (Near East University
    Chongqing Normal University)

  • Yekini Shehu

    (Zhejiang Normal University)

Abstract

In this paper, we design strongly convergent golden ratio algorithms to solve variational inequalities in Hilbert spaces. We give strong convergence results in both cases when the stepsizes are constant and when the step sizes are self-adaptively generated. Our proposed algorithms have the same feature of one evaluation of the proximal operator and one evaluation of the cost operator at each iteration, just like the weakly convergent golden ratio algorithm. We test our proposed algorithms with some standard numerical examples and make some numerical comparisons with other related algorithms on variational inequalities in the literature.

Suggested Citation

  • Yonghong Yao & Abubakar Adamu & Yekini Shehu, 2025. "Strongly Convergent Golden Ratio Algorithms for Variational Inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 101(3), pages 395-433, June.
    • Handle: RePEc:spr:mathme:v:101:y:2025:i:3:d:10.1007_s00186-025-00896-1
    DOI: 10.1007/s00186-025-00896-1
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