Fast Convergence of Dynamical ADMM via Time Scaling of Damped Inertial Dynamics
In this paper, we propose in a Hilbertian setting a second-order time-continuous dynamic system with fast convergence guarantees to solve structured convex minimization problems with an affine constraint. The system is associated with the augmented Lagrangian formulation of the minimization problem....
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| Veröffentlicht in: | Journal of optimization theory and applications 2022-06, Vol.193 (1-3), p.704-736 |
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| container_title | Journal of optimization theory and applications |
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| creator | Attouch, Hedy Chbani, Zaki Fadili, Jalal Riahi, Hassan |
| description | In this paper, we propose in a Hilbertian setting a second-order time-continuous dynamic system with fast convergence guarantees to solve structured convex minimization problems with an affine constraint. The system is associated with the augmented Lagrangian formulation of the minimization problem. The corresponding dynamics brings into play three general time-varying parameters, each with specific properties, and which are, respectively, associated with viscous damping, extrapolation and temporal scaling. By appropriately adjusting these parameters, we develop a Lyapunov analysis which provides fast convergence properties of the values and of the feasibility gap. These results will naturally pave the way for developing corresponding accelerated ADMM algorithms, obtained by temporal discretization. |
| doi_str_mv | 10.1007/s10957-021-01859-2 |
| format | Article |
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The system is associated with the augmented Lagrangian formulation of the minimization problem. The corresponding dynamics brings into play three general time-varying parameters, each with specific properties, and which are, respectively, associated with viscous damping, extrapolation and temporal scaling. By appropriately adjusting these parameters, we develop a Lyapunov analysis which provides fast convergence properties of the values and of the feasibility gap. 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The system is associated with the augmented Lagrangian formulation of the minimization problem. The corresponding dynamics brings into play three general time-varying parameters, each with specific properties, and which are, respectively, associated with viscous damping, extrapolation and temporal scaling. By appropriately adjusting these parameters, we develop a Lyapunov analysis which provides fast convergence properties of the values and of the feasibility gap. These results will naturally pave the way for developing corresponding accelerated ADMM algorithms, obtained by temporal discretization.</description><subject>Algorithms</subject><subject>Applications of Mathematics</subject><subject>Approximation</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Computer Science</subject><subject>Convergence</subject><subject>Convex analysis</subject><subject>Dynamical Systems</subject><subject>Engineering</subject><subject>Lagrange multiplier</subject><subject>Machine Learning</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Methods</subject><subject>Operations Research/Decision Theory</subject><subject>Optimization</subject><subject>Optimization and Control</subject><subject>Parameters</subject><subject>Signal and Image Processing</subject><subject>Statistics</subject><subject>Theory of Computation</subject><subject>Viscosity</subject><subject>Viscous 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| subjects | Algorithms Applications of Mathematics Approximation Calculus of Variations and Optimal Control Optimization Computer Science Convergence Convex analysis Dynamical Systems Engineering Lagrange multiplier Machine Learning Mathematics Mathematics and Statistics Methods Operations Research/Decision Theory Optimization Optimization and Control Parameters Signal and Image Processing Statistics Theory of Computation Viscosity Viscous damping |
| title | Fast Convergence of Dynamical ADMM via Time Scaling of Damped Inertial Dynamics |
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