Strongly Convergent Golden Ratio Algorithms for Variational Inequalities

Yonghong Yao (), Abubakar Adamu () and Yekini Shehu ()
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Yonghong Yao: Tiangong University
Abubakar Adamu: Near East University
Yekini Shehu: Zhejiang Normal University

Mathematical Methods of Operations Research, 2025, vol. 101, issue 3, No 2, 395-433

Abstract: 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.

Keywords: Variational inequalities; Monotone operators; Strong convergence; Proximal operator; 47H09; 47H10; 49J20; 49J40 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00186-025-00896-1

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