Extragradient Sliding for Composite Non-Monotone Variational Inequalities

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 $\epsilon$-accuracy of the solution, the oracle complexity of the non-monotone operator $Q$ for our algorithm is $O\left(L_p^2/{\epsilon }^2\right)$ in contrast to the basic Extragradient algorithm with $O\left((L_p+L_q{)}^2/{\epsilon }^2\right)$. The results of numerical experiments confirm the theoretical findings and show the superiority of the proposed method.

12 pages, 1 algorithm, 3 figures

References in corpus (1)

• Smooth Monotone Stochastic Variational Inequalities and Saddle Point Problems: A Survey