CAPPA: Continuous-Time Accelerated Proximal Point Algorithm for Sparse Recovery
Kunal Garg, Mayank Baranwal
Abstract
This letter 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. Most existing algorithms for solving $\ell _1$-minimization problems are discrete-time 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 outperforms Locally Competitive Algorithm (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.