2024/01/27 by Min Tao, Xiaoping Zhang, Tao, Min +3 · 1 citation
Computer Science · Decision Sciences · Mathematics · #FOS: Mathematics #Limits and Structures in Graph Theory #Optimization and Control (math.OC) #Optimization and Search Problems #Scheduling and Timetabling Solutions
paper · pdf · doi:10.48550/arxiv.2401.15405
openalex publication_date 2024/01/27 · openalex created_date 2024/01/31 · openalex updated_date 2026/08/01
The L1/L2 norm ratio arose as a sparseness measure and attracted a considerable amount of attention due to three merits: (i) sharper approximations of L0 compared to the L1; (ii) parameter-free and scale-invariant; (iii) more attractive than L1 under highly-coherent matrices. In this paper, we first establish the partly smooth property of L1 over L2 minimization relative to an active manifold \cal M and also demonstrate its prox-regularity property. Second, we reveal that ADMMp (or ADMM+p) can identify the active manifold within a finite iterations. This discovery contributes to a deeper understanding of the optimization landscape associated with L1 over L2 minimization. Third, we propose a novel heuristic algorithm framework that combines ADMMp (or ADMM+p) with a globalized semismooth Newton method tailored for the active manifold \cal M. This hybrid approach leverages the strengths of both methods to enhance convergence. Finally, through extensive numerical simulations, we showcase the superiority of our heuristic algorithm over existing state-of-the-art methods for sparse recovery.