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arXiv · 2603.06442

The Popov's Algorithm with Optimal Bounded Stepsize for Generalized Monotone Variational Inequalities

Nhung Hong Nguyen·Thanh Quoc Trinh·Phan Tu Vuong
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Abstract

For solving constrained (pseudo)-monotone variational inequality, we prove that the upper bound of stepsize $\frac{1}{2L}$ established for the Popov's algorithm and the forward-reflected-backward algorithm is tight. For unconstrained case, we can enlarge the upper bound to $\frac{1}{\sqrt{3}L}$ and show that this upper bound is also tight. The convergence analysis is carried out by using a new Lyapunov-type function.

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Nhung Hong Nguyen, Thanh Quoc Trinh, Phan Tu Vuong. 2026-03-06. The Popov's Algorithm with Optimal Bounded Stepsize for Generalized Monotone Variational Inequalities. https://arxiv.org/abs/2603.06442

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