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Prox-Method with Rate of Convergence O(1/t) for Variational Inequalities with Lipschitz Continuous Monotone Operators and Smooth Convex-Concave Saddle Point Problems
Abstract
We propose a prox-type method with efficiency estimate $O(\epsilon^{-1})$ for approximating saddle points of convex-concave C$^{1,1}$ functions and solutions of variational inequalities with monotone Lipschitz continuous operators. Application examples include matrix games, eigenvalue minimization, and computing the Lovasz capacity number of a graph, and these are illustrated by numerical experiments with large-scale matrix games and Lovasz capacity problems.
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Cited by
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Chambolle, A., & Pock, T. (2011) · Journal of Mathematical Imaging and Vision · doi:10.1007/s10851-010-0251-1 · Cited by 4,336
An optimal method for stochastic composite optimization
Lan, G. (2012) · Mathematical Programming · doi:10.1007/s10107-010-0434-y · Cited by 427
Over-the-Air Computation via Reconfigurable Intelligent Surface
Fang, W., Jiang, Y., Shi, Y., Zhou, Y., Chen, W., & Letaief, K. B. (2021) · IEEE Transactions on Communications · doi:10.1109/tcomm.2021.3114791 · Cited by 93
Metadata
- Authors
- Nemirovski, A.
- Venue
- SIAM Journal on Optimization
- Published
- 2004-01
- Volume
- 15
- Issue
- 1
- Pages
- 229-251
- ISSN
- 1052-6234 (ISSN-L)
- 1095-7189
- OpenAlex
- W2089559088
- Cited by
- 750
- References
- 0
- FWCI
- 10.20
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Prox-Method with Rate of Convergence O(1/t) for Variational Inequalities with Lipschitz Continuous Monotone Operators and Smooth Convex-Concave Saddle Point Problems. https://app.cochat.ai/papers/10.1137/s1052623403425629
- The paper
- Nemirovski, A. (2004). Prox-Method with Rate of Convergence O(1/t) for Variational Inequalities with Lipschitz Continuous Monotone Operators and Smooth Convex-Concave Saddle Point Problems. SIAM Journal on Optimization. https://doi.org/10.1137/s1052623403425629
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