Fast convex optimization via inertial dynamics with Hessian driven damping

We first study the fast minimization properties of the trajectories of the second-order evolution equationx¨(t)+αtx˙(t)+β∇2Φ(x(t))x˙(t)+∇Φ(x(t))=0, where Φ:H→R is a smooth convex function acting on a real Hilbert space H, and α, β are positive parameters. This inertial system combines an isotropic v...

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Bibliographic Details

Published in:	Journal of Differential Equations Vol. 261; no. 10; pp. 5734 - 5783
Main Authors:	Attouch, Hedy, Peypouquet, Juan, Redont, Patrick
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 15.11.2016 Elsevier
Subjects:	Convex optimization Fast convergent methods Forward–backward algorithm Gradient flows Hessian-driven damping Inertial dynamics Mathematics Gradient flows Inertial dynamics Convex optimization Hessian-driven damping Fast convergent methods Forward–backward algorithm Gradient flowsInertial dynamics
ISSN:	0022-0396, 1090-2732
Online Access:	Get full text
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