تقرير
Bregman Golden Ratio Algorithms for Variational Inequalities
| العنوان: | Bregman Golden Ratio Algorithms for Variational Inequalities |
|---|---|
| المؤلفون: | Tam, Matthew K., Uteda, Daniel J. |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, 47J20, 49J40, 65K15, 65Y20 |
| الوصف: | Variational inequalities provide a framework through which many optimisation problems can be solved, in particular, saddle-point problems. In this paper, we study modifications to the so-called Golden RAtio ALgorithm (GRAAL) for variational inequalities -- a method which uses a fully explicit adaptive step-size, and provides convergence results under local Lipschitz assumptions without requiring backtracking. We present and analyse two Bregman modifications to GRAAL: the first uses a fixed step-size and converges under global Lipschitz assumptions, and the second uses an adaptive step-size rule. Numerical performance of the former method is demonstrated on a bimatrix game arising in network communication, and of the latter on two problems, namely, power allocation in Gaussian communication channels and $N$-person Cournot completion games. In all of these applications, an appropriately chosen Bregman distance simplifies the projection steps computed as part of the algorithm. Comment: 24 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2208.05102 |
| رقم الأكسشن: | edsarx.2208.05102 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |