论文标题
CAPPA：连续的时间加速近端算法，用于稀疏恢复
CAPPA: Continuous-time Accelerated Proximal Point Algorithm for Sparse Recovery
论文作者
论文摘要
本文为$ \ ell_1 $ - 毫米化问题开发了一种新颖的连续时间加速近端算法（CAPPA），具有可证明的固定时间收敛保证。 $ \ ell_1 $ - 最小化的问题出现在几种情况下，例如压缩感应（CS）理论中的稀疏恢复（SR），以及机器学习中的稀疏线性和逻辑回归以命名一些。用于解决$ \ ell_1 $最小化问题的大多数现有算法是离散的时间，效率低下且需要详尽的计算机引导的迭代。 CAPPA在两个方面减轻了这个问题：（a）它涵盖了可以使用模拟电路实现的连续时间算法； （b）通过向最佳解决方案展示可证明的固定时间收敛性，它可以更好地改善LCA和有限的LCA（最近开发的连续时间动力学系统来解决SR问题）。因此，CAPPA更适合快速有效地处理SR问题。提出了模拟研究证实了CAPPA的计算优势。
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.
