A Dynamical Approach to Two-Block Separable Convex Optimization Problems with Linear Constraints. (13th November 2020)

• Record Type: Journal Article
• Authors: Bitterlich, Sandy; Csetnek, Ernö Robert; Wanka, Gert
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 1(2021)
• Page Start: 1
• Page End: 38
• Publication Date: 2020-11-13
• Subjects: Convex optimization -- duality -- dynamical system -- Lyapunov analysis -- Lagrangian -- primal dual algorithm -- Proximal AMA -- saddle points -- structured convex minimization -- subdifferential; 37N40 -- 49N15 -- 90C25 -- 90C46; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1845730
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: The aim of this manuscript is to approach by means of first order differential equations/inclusions convex programming problems with two-block separable linear constraints and objectives, whereby (at least) one of the components of the latter is assumed to be strongly convex. Each block of the objective contains a further smooth convex function. We investigate the dynamical system proposed and prove that its trajectories converge weakly to a saddle point of the Lagrangian of the convex optimization problem. The dynamical system provides through time discretization the alternating minimization algorithm AMA and also its proximal variant recently introduced in the literature.