A Dynamical Approach to Two-Block Separable Convex Optimization Problems with Linear Constraints
| Autor: | Sandy Bitterlich, Ernö Robert Csetnek, Gert Wanka |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Control and Optimization
Lyapunov analysis Duality (optimization) Subderivative Dynamical system 01 natural sciences dynamical system Separable space 37N40 49N15 90C25 90C46 Block (programming) Saddle point FOS: Mathematics Applied mathematics 0101 mathematics Proximal AMA Mathematics - Optimization and Control Lagrangian Mathematics structured convex minimization 010102 general mathematics subdifferential saddle points Computer Science Applications Convex optimization 010101 applied mathematics Optimization and Control (math.OC) Ordinary differential equation primal dual algorithm Signal Processing duality Analysis |
| Popis: | 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 asymptotically converge to a saddle point of the Lagrangian of the convex optimization problem. Time discretization of the dynamical system leads to the alternating minimization algorithm AMA and also to its proximal variant recently introduced in the literature. Comment: 30 pages, 2 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|