Stochastic golden ratio algorithm to non-convex stochastic mixed variational inequality problem

Shenghua Wang (), Ziqi Zhu and Lanxiang Yu
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Shenghua Wang: Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University
Ziqi Zhu: Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University
Lanxiang Yu: Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University

Journal of Global Optimization, 2025, vol. 91, issue 4, No 6, 829-850

Abstract: Abstract In [Grad and Lara, J. Optim. Theory Appl. 190(2), 565–580 (2021)], the authors proposed a golden ratio algorithm for solving the deterministic mixed variational inequality problem with prox-convex function. In this paper, we study a new class of stochastic mixed variational inequality problems with the expectation of a prox-convex stochastic function and present a stochastic golden ratio algorithm for solving the proposed problem. The convergence and the convergence rate of our algorithm are shown under some simple and necessary conditions. Finally, we present some numerical examples to illustrate the efficiency of the proposed algorithm.

Keywords: Stochastic variational inequalities; Mixed variational inequalities; Stochastic approximations; Golden Ratio Algorithms; 54E70; 65K15; 62L20; 93E35; 90C33 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10898-024-01445-6

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