Parallel Multi-Block ADMM with o(1 / k) Convergence

• Published in: Journal of scientific computing Vol. 71; no. 2; pp. 712 - 736
• Main Authors: Deng, Wei, Lai, Ming-Jun, Peng, Zhimin, Yin, Wotao
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.05.2017; Springer Nature B.V
• Subjects: Algorithms; Computational Mathematics and Numerical Analysis; Convergence; Convex analysis; Decomposition; Guarantees; Lagrange multiplier; Mathematical analysis; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Matrices (mathematics); Optimization; Parameters; Theoretical; Variables; Convergence rate; Alternating direction method of multipliers; Parallel and distributed computing; ADMM
• ISSN: 0885-7474; 1573-7691
• DOI: 10.1007/s10915-016-0318-2

This paper introduces a parallel and distributed algorithm for solving the following minimization problem with linear constraints: minimize f 1 ( x 1 ) + ⋯ + f N ( x N ) subject to A 1 x 1 + ⋯ + A N x N = c , x 1 ∈ X 1 , … , x N ∈ X N , where N ≥ 2 , f i are convex functions, A i are matrices, and X...