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arXiv · 2403.14981

Extragradient Sliding for Composite Non-Monotone Variational Inequalities

Roman Emelyanov·Andrey Tikhomirov·Aleksandr Beznosikov·Alexander Gasnikov
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Abstract

Variational inequalities offer a versatile and straightforward approach to analyzing a broad range of equilibrium problems in both theoretical and practical fields. In this paper, we consider a composite generally non-monotone variational inequality represented as a sum of $L_q$-Lipschitz monotone and $L_p$-Lipschitz generally non-monotone operators. We applied a special sliding version of the classical Extragradient method to this problem and obtain better convergence results. In particular, to achieve $\varepsilon$-accuracy of the solution, the oracle complexity of the non-monotone operator $Q$ for our algorithm is $O\left(L_p^2/\varepsilon^2\right)$ in contrast to the basic Extragradient algorithm with $O\left((L_p+L_q)^2/\varepsilon^2\right)$. The results of numerical experiments confirm the theoretical findings and show the superiority of the proposed method.

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Roman Emelyanov, Andrey Tikhomirov, Aleksandr Beznosikov, Alexander Gasnikov. 2024-03-22. Extragradient Sliding for Composite Non-Monotone Variational Inequalities. https://doi.org/10.1007/978-3-031-79119-2_7

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