CAPPA: Continuous-time Accelerated Proximal Point Algorithm for Sparse Recovery

TL;DR

This paper introduces CAPPA, a novel continuous-time algorithm with fixed-time convergence for sparse recovery problems, offering advantages over existing discrete and continuous methods in efficiency and implementation.

Contribution

The paper proposes CAPPA, a continuous-time accelerated proximal point algorithm with fixed-time convergence for -minimization, improving efficiency and implementation over existing methods.

Findings

CAPPA demonstrates fixed-time convergence in simulations.

CAPPA outperforms LCA and finite-time LCA in computational efficiency.

Simulation results confirm the practical advantages of CAPPA.

Abstract

This paper develops a novel Continuous-time Accelerated Proximal Point Algorithm (CAPPA) for $\ell_1$-minimization problems with provable fixed-time convergence guarantees. The problem of $\ell_1$-minimization appears in several contexts, such as sparse recovery (SR) in Compressed Sensing (CS) theory, and sparse linear and logistic regressions in machine learning to name a few. Most existing algorithms for solving $\ell_1$-minimization problems are discrete-time, inefficient and require exhaustive computer-guided iterations. CAPPA alleviates this problem on two fronts: (a) it encompasses a continuous-time algorithm that can be implemented using analog circuits; (b) it betters LCA and finite-time LCA (recently developed continuous-time dynamical systems for solving SR problems) by exhibiting provable fixed-time convergence to optimal solution. Consequently, CAPPA is better suited for fast and efficient handling of SR problems. Simulation studies are presented that corroborate computational advantages of CAPPA.