Communications in Mathematical Sciences
Volume 13 (2015)
A dual algorithm for a class of augmented convex signal recovery models
Pages: 103 – 112
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. Extensions to models with gauge functions are provided.
augmented convex model, Lagrange dual, primal-dual, proximal operator, gauge, signal recovery
2010 Mathematics Subject Classification