On the convergence properties of a majorized ADMM for linearly constrained convex optimization problems with coupled objective functions

作者: Ying Cui , Defeng Sun , Kim-Chuan Toh , Xudong Li

DOI:

关键词:

摘要: … (ADMM) for linearly constrained convex optimization problems whose objectives contain coupled … step length to the linearly constrained convex optimization problem with a quadratically …

参考文章(14)
Meisam Razaviyayn, Mingyi Hong, Zhi-Quan Luo, Shiqian Ma, Tsung-Hui Chang, Xiangfeng Wang, A Block Successive Upper Bound Minimization Method of Multipliers for Linearly Constrained Convex Optimization arXiv: Optimization and Control. ,(2014)
Bingsheng He, Xiaoming Yuan, On the $O(1/n)$ Convergence Rate of the Douglas-Rachford Alternating Direction Method SIAM Journal on Numerical Analysis. ,vol. 50, pp. 700- 709 ,(2012) , 10.1137/110836936
Caihua Chen, Bingsheng He, Yinyu Ye, Xiaoming Yuan, The direct extension of ADMM for multi-block convex minimization problems is not necessarily convergent Mathematical Programming. ,vol. 155, pp. 57- 79 ,(2016) , 10.1007/S10107-014-0826-5
Jean-Baptiste Hiriart-Urruty, Jean-Jacques Strodiot, V. Hien Nguyen, Generalized Hessian matrix and second-order optimality conditions for problems with C 1,1 data Applied Mathematics and Optimization. ,vol. 11, pp. 43- 56 ,(1984) , 10.1007/BF01442169
Yu. Nesterov, Gradient methods for minimizing composite functions Mathematical Programming. ,vol. 140, pp. 125- 161 ,(2013) , 10.1007/S10107-012-0629-5
Daniel Gabay, Bertrand Mercier, A dual algorithm for the solution of nonlinear variational problems via finite element approximation Computers & Mathematics with Applications. ,vol. 2, pp. 17- 40 ,(1976) , 10.1016/0898-1221(76)90003-1
Jonathan Eckstein, Dimitri P. Bertsekas, On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators Mathematical Programming. ,vol. 55, pp. 293- 318 ,(1992) , 10.1007/BF01581204
Xudong Li, Defeng Sun, Kim-Chuan Toh, A Schur complement based semi-proximal ADMM for convex quadratic conic programming and extensions Mathematical Programming. ,vol. 155, pp. 333- 373 ,(2016) , 10.1007/S10107-014-0850-5
Renato D. C. Monteiro, Benar F. Svaiter, ITERATION-COMPLEXITY OF BLOCK-DECOMPOSITION ALGORITHMS AND THE ALTERNATING DIRECTION METHOD OF MULTIPLIERS ∗ Siam Journal on Optimization. ,vol. 23, pp. 475- 507 ,(2013) , 10.1137/110849468
Damek Davis, Wotao Yin, Convergence Rate Analysis of Several Splitting Schemes arXiv: Optimization and Control. pp. 115- 163 ,(2016) , 10.1007/978-3-319-41589-5_4