期刊
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
卷 188, 期 1, 页码 1-25出版社
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10957-020-01782-y
关键词
Linear convergence; Alternating direction method of multipliers; Error bound; Nonconvex minimization
资金
- National Natural Science Foundation of China [11625105, 11431002, 11801279, 11871279, 11571178]
- Natural Science Foundation of Jiangsu Province [BK20180782]
- Startup Foundation for Introducing Talent of NUIST [2017r059]
In this paper, the convergence rate of the alternating direction method of multipliers for solving nonconvex separable optimization problems is considered. It is proven that the sequence generated by this method converges locally to a critical point of the nonconvex optimization problem with a linear convergence rate. Results are illustrated through the application of this method to nonconvex quadratic programming problems and comparison with other state-of-the-art algorithms.
In this paper, we consider the convergence rate of the alternating direction method of multipliers for solving the nonconvex separable optimization problems. Based on the error bound condition, we prove that the sequence generated by the alternating direction method of multipliers converges locally to a critical point of the nonconvex optimization problem in a linear convergence rate, and the corresponding sequence of the augmented Lagrangian function value converges in a linear convergence rate. We illustrate the analysis by applying the alternating direction method of multipliers to solving the nonconvex quadratic programming problems with simplex constraint, and comparing it with some state-of-the-art algorithms, the proximal gradient algorithm, the proximal gradient algorithm with extrapolation, and the fast iterative shrinkage-thresholding algorithm.
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