A primal-dual fixed point algorithm for multi-block convex minimization

TL;DR

This paper extends a primal-dual fixed point algorithm to efficiently solve multi-block convex minimization problems, demonstrating its flexibility, convergence guarantees, and effectiveness in large-scale signal processing and imaging applications.

Contribution

The paper introduces a generalized PDFP algorithm for multi-block problems, showing its applicability, convergence, and advantages over existing methods like ADMM.

Findings

PDFP can be applied to multi-block convex problems with convergence guarantees.

The algorithm enables fully decoupled, parallelizable schemes for large-scale problems.

Experimental results demonstrate competitive performance of PDFP-based schemes.

Abstract

We extend a primal-dual fixed point algorithm (PDFP) proposed in [5] to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP algorithm to multi-block problems and illustrate how practical and fully decoupled schemes can be derived, especially for parallel implementation of large scale problems. The connections and comparisons to the alternating direction method of multiplier (ADMM) are also present. We demonstrate how different algorithms can be obtained by splitting the problems in different ways through the classic example of sparsity regularized least square model with constraint. In particular, for a class of linearly constrained problems, which are of great interest in the context of multi-block ADMM, can be solved by PDFP with a guarantee of convergence. Finally, some experiments are provided to illustrate the performance of several schemes derived by the PDFP algorithm.