Fast convergence of dynamical ADMM via time scaling of damped inertial dynamics

DOI10.1007/s10957-021-01859-2zbMath1497.37122arXiv2103.12675OpenAlexW3157095133MaRDI QIDQ2139279

Zaki Chbani, Hassan Riahi, Hedy Attouch, Jalal Fadili

Publication date: 17 May 2022

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.12675

zbMATH Keywords

ADMMconvergence ratesaugmented LagrangianLyapunov analysisconvex constrained minimizationdamped inertial dynamicsNesterov accelerated gradient methodtemporal scaling

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Convex programming (90C25) Numerical optimization and variational techniques (65K10) Management decision making, including multiple objectives (90B50) Applications of functional analysis in optimization, convex analysis, mathematical programming, economics (46N10) Dynamical systems in optimization and economics (37N40) Approximation methods and numerical treatment of dynamical systems (37M99)

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Fast augmented Lagrangian method in the convex regime with convergence guarantees for the iterates ⋮ Inertial primal-dual dynamics with damping and scaling for linearly constrained convex optimization problems ⋮ On Proximal Algorithms with Inertial Effects Beyond Monotonicity ⋮ Convergence of inertial dynamics driven by sums of potential and nonpotential operators with implicit Newton-like damping ⋮ Time rescaling of a primal-dual dynamical system with asymptotically vanishing damping ⋮ A second order primal-dual dynamical system for a convex-concave bilinear saddle point problem ⋮ Optimal convergence rates for damped inertial gradient dynamics with flat geometries ⋮ Convergence Rates of Inertial Primal-Dual Dynamical Methods for Separable Convex Optimization Problems ⋮ Fast primal-dual algorithm via dynamical system for a linearly constrained convex optimization problem

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