تقرير
Extragradient Sliding for Composite Non-Monotone Variational Inequalities
| العنوان: | Extragradient Sliding for Composite Non-Monotone Variational Inequalities |
|---|---|
| المؤلفون: | Emelyanov, Roman, Tikhomirov, Andrey, Beznosikov, Aleksandr, Gasnikov, Alexander |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control |
| الوصف: | 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. Comment: 12 pages, 1 algorithm, 3 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.14981 |
| رقم الأكسشن: | edsarx.2403.14981 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |