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Bregman-Golden Ratio Algorithms for Variational Inequalities.
- Source :
-
Journal of Optimization Theory & Applications . Dec2023, Vol. 199 Issue 3, p993-1021. 29p. - Publication Year :
- 2023
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00223239
- Volume :
- 199
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Journal of Optimization Theory & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 173765990
- Full Text :
- https://doi.org/10.1007/s10957-023-02320-2