Convergence of Bregman ADMM for solving multi-block nonconvex separable optimization problems
Xia Haoming et al.
What the paper says
(Communicated by Xinmin Yang) Abstract: The alternating direction method of multipliers (ADMM) has demonstrated its efficiency and well-understood convergence properties when applied to minimization problems where the objective function is the sum of two nonconvex separable functions and the constraint is linear. However, the requirement for global Lipschitz continuity of the gradient of differentiable functions, which is often impractical in nonconvex optimization problems, restricts its applicability across various domains. Recently, a novel Bregman ADMM has been introduced for two-block nonconvex optimization problems with linear constraints. This new Bregman ADMM not only removes the need for global Lipschitz continuity of the gradient, making it suitable for a broader range of practical problems, but also ensures that it can reduce to the classical ADMM in specific cases. Building on this Bregman ADMM, we address multi-block nonconvex separable optimization problems with linear constraints. We demonstrate that any cluster point of the iterative sequence generated by Bregman ADMM is a critical point, provided that the associated function satisfies the Kurdyka-Łojasiewicz inequality. Additionally, we present sufficient conditions to ensure both the convergence and convergence rate of the algorithm.
Evidence weight
Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40
| F · citation impact | 0.50 × 0.4 = 0.20 |
| M · momentum | 0.50 × 0.15 = 0.07 |
| V · venue signal | 0.50 × 0.05 = 0.03 |
| R · text relevance † | 0.50 × 0.4 = 0.20 |
† Text relevance is estimated at 0.50 on the detail page — for your query’s actual relevance score, open this paper from a search result.