A New Infeasible Projection Method for Stochastic Variational Inequality Problem

Shenghua Wang (), Yueyao Zhang () and Yeol Je Cho ()
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Shenghua Wang: North China Electric Power University
Yueyao Zhang: North China Electric Power University
Yeol Je Cho: Gyeongsang National University

Journal of Optimization Theory and Applications, 2026, vol. 208, issue 1, No 6, 28 pages

Abstract: Abstract In this paper, we propose a new infeasible stochastic approximation projection method based on the golden ratio for a nonmonotone stochastic variational inequality problem. In the traditional golden ratio methods, the constant $$\phi $$ ϕ is taken as $$\frac{1+\sqrt{5}}{2}$$ 1 + 5 2 . However, the constant is relaxed to the interval $$(1,\infty )$$ ( 1 , ∞ ) in our method. A new self-adaptive step size which is admitted to be increasing is generated for dealing with the unknown Lipschitz constant of the mapping. The almost sure convergence and convergence rate of the proposed method are shown. Some numerical examples are given to illustrate the competitiveness of our algorithm compared to the related algorithms in the literature. Finally, we apply our method to solve a network bandwidth allocation problem.

Keywords: Stochastic variational inequality; Stochastic approximation; Golden ratio method; Projection method; 65K15; 90C33; 90C15; 62L20 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/s10957-025-02825-y

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