Proximal Regularization for the Saddle Point Gradient Dynamics
This article concerns the solution of a convex optimization problem through the saddle point gradient dynamics. Instead of using the standard Lagrangian as is classical in this method, we consider a regularized Lagrangian obtained through a proximal minimization step. We show that, without assumptio...
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| Veröffentlicht in: | IEEE transactions on automatic control 2021-09, Vol.66 (9), p.4385-4392 |
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| container_title | IEEE transactions on automatic control |
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| creator | Goldsztajn, Diego Paganini, Fernando |
| description | This article concerns the solution of a convex optimization problem through the saddle point gradient dynamics. Instead of using the standard Lagrangian as is classical in this method, we consider a regularized Lagrangian obtained through a proximal minimization step. We show that, without assumptions of smoothness or strict convexity in the original problem, the regularized Lagrangian is smooth and leads to globally convergent saddle point dynamics. The method is demonstrated through an application to resource allocation in cloud computing. |
| doi_str_mv | 10.1109/TAC.2020.3045124 |
| format | Article |
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| language | eng |
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| source | IEEE Electronic Library (IEL) |
| subjects | Asymptotic stability Cloud computing Computational geometry Control theory Convergence Convex functions Convex optimization Convexity Optimization proximal method Regularization Resource allocation Resource management saddle point dynamics Saddle points Smoothness Trajectory |
| title | Proximal Regularization for the Saddle Point Gradient Dynamics |
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