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CAPPA Continuous-time Accelerated Proximal Point Algorithm for Sparse Recovery

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Document pages: 6 pages

Abstract: This paper develops a novel Continuous-time Accelerated Proximal PointAlgorithm (CAPPA) for $ ell 1$-minimization problems with provable fixed-timeconvergence guarantees. The problem of $ ell 1$-minimization appears in severalcontexts, such as sparse recovery (SR) in Compressed Sensing (CS) theory, andsparse linear and logistic regressions in machine learning to name a few. Mostexisting algorithms for solving $ ell 1$-minimization problems arediscrete-time, inefficient and require exhaustive computer-guided iterations.CAPPA alleviates this problem on two fronts: (a) it encompasses acontinuous-time algorithm that can be implemented using analog circuits; (b) itbetters LCA and finite-time LCA (recently developed continuous-time dynamicalsystems for solving SR problems) by exhibiting provable fixed-time convergenceto optimal solution. Consequently, CAPPA is better suited for fast andefficient handling of SR problems. Simulation studies are presented thatcorroborate computational advantages of CAPPA.

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