A dual algorithm for a class of augmented convex models

TL;DR

This paper introduces a dual gradient algorithm for augmented convex models, unifying existing algorithms like linearized Bregman and singular value thresholding, with proven convergence properties.

Contribution

It proposes a new dual gradient algorithm for augmented convex models, generalizing and improving upon existing methods with a unified convergence analysis.

Findings

The algorithm includes linearized Bregman and singular value thresholding as special cases.

The convergence of primal and dual sequences is rigorously established.

The approach simplifies the analysis of augmented convex models.

Abstract

Convex optimization models find interesting applications, especially in signal/image processing and compressive sensing. We study some augmented convex models, which are perturbed by strongly convex functions, and propose a dual gradient algorithm. The proposed algorithm includes the linearized Bregman algorithm and the singular value thresholding algorithm as special cases. Based on fundamental properties of proximal operators, we present a concise approach to establish the convergence of both primal and dual sequences, improving the results in the existing literature.