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• W2885153985 abstract "The acceleration technique introduced by Nesterov for gradient descent is widely used in machine learning, but its principles are not yet fully understood. Recently, significant progress has been made to close this understanding gap through a continuous-time dynamical systems perspective associated with gradient methods for smooth and unconstrained problems. Here we extend this perspective to nonsmooth and linearly constrained problems by deriving nonsmooth dynamical systems related to variants of the relaxed and accelerated alternating direction method of multipliers (ADMM). We introduce two new ADMM variants, one based on Nesterov's acceleration and the other inspired by Polyak's heavy ball method, and derive differential inclusions modelling these algorithms in the continuous-time limit. Using a nonsmooth Lyapunov analysis, we obtain rate-of-convergence results for these dynamical systems in the convex and strongly convex setting that illustrate an interesting tradeoff between Nesterov and heavy ball acceleration." @default.
• W2885153985 created "2018-08-22" @default.
• W2885153985 creator A5079880652 @default.
• W2885153985 creator A5082367556 @default.
• W2885153985 creator A5016481949 @default.
• W2885153985 date "2018-08-13" @default.
• W2885153985 modified "2023-09-27" @default.
• W2885153985 title "A Dynamical Systems Perspective on Nonsmooth Constrained Optimization" @default.
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• W2885153985 hasPublicationYear "2018" @default.
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