2024/02/03 by Zekun Liu, Liu, Zekun
Business, Management and Accounting · Computer Science · Engineering · #65K10 #90C26 #90C90 #Advanced Manufacturing and Logistics Optimization #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Optimization and Control (math.OC) #Optimization and Search Problems #Supply Chain and Inventory Management
paper · pdf · doi:10.48550/arxiv.2402.02193
openalex publication_date 2024/02/03 · openalex created_date 2024/02/08 · openalex updated_date 2026/07/28
We consider a 3-block Alternating Direction Method of Multipliers (ADMM) for solving nonconvex nonseparable problems with a linear constraint. Inspired by \cite[Sun, Toh and Yang, SIAM Journal on Optimization, 25 (2015), pp.882-915]wtwice, the proposed ADMM follows the Block Coordinate Descent (BCD) cycle order 1→ 3→ 2→ 3. We analyze its convergence based on the Kurdyka-Łojasiewicz property. We also discuss two useful extensions of the proposed ADMM with 2→ 3→ 1→ 3 Gauss-Seidel BCD cycle order, and with adding a proximal term for more general nonseparable problems, respectively. Moreover, we make numerical experiments on two nonconvex problems: robust principal component analysis and nonnegative matrix completion. Results show the efficiency and outperformance of the proposed ADMM.