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Asymptotic convergence of constrained primal–dual dynamics
Open accessAbstract
This paper studies the asymptotic convergence properties of the primal-dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by providing an example that rules out the possibility of employing the invariance principle for hybrid automata to study asymptotic convergence. We understand the solutions of the primal-dual dynamics in the Caratheodory sense and characterize their existence, uniqueness, and continuity with respect to the initial condition. We use the invariance principle for discontinuous Caratheodory systems to establish that the primal-dual optimizers are globally asymptotically stable under the primal-dual dynamics and that each solution of the dynamics converges to an optimizer.
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Citations
Cited by
Yi, P., Hong, Y., & Liu, F. (2016) · Automatica · doi:10.1016/j.automatica.2016.08.007 · Cited by 478
Delay-Robust Primal-Dual Dynamics for Distributed Optimization
Şen, G. D., Machado, J. E., Öke Günel, G., & Schiffer, J. (2026) · IEEE Control Systems Letters · doi:10.1109/lcsys.2026.3698431
Wang, X., & Chen, X. (2026) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2026.3684791
Metadata
- Authors
- Cherukuri, A., Mallada, E., & Cortés, J.
- Venue
- Systems & Control Letters
- Publisher
- Elsevier BV
- Published
- 2016-01
- Volume
- 87
- Pages
- 10-15
- ISSN
- 0167-6911 (ISSN-L)
- OpenAlex
- W2122356478
- Cited by
- 189
- References
- 0
- FWCI
- 17.63
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Cherukuri, A., Mallada, E., & Cortés, J. (2016). Asymptotic convergence of constrained primal–dual dynamics. Systems & Control Letters. https://doi.org/10.1016/j.sysconle.2015.10.006
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