期刊
MATHEMATICAL PROGRAMMING
卷 141, 期 1-2, 页码 349-382出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s10107-012-0530-2
关键词
Convex optimization; Variable splitting; Alternating linearization method; Alternating direction method; Augmented Lagrangian method; Optimal gradient method; Gauss-Seidel method; Peaceman-Rachford method
类别
资金
- NSF [DMS 06-06712, DMS 10-16571]
- ONR [N00014-08-1-1118]
- DOE [DE-FG02-08ER25856]
We present in this paper alternating linearization algorithms based on an alternating direction augmented Lagrangian approach for minimizing the sum of two convex functions. Our basic methods require at most iterations to obtain an -optimal solution, while our accelerated (i.e., fast) versions of them require at most iterations, with little change in the computational effort required at each iteration. For both types of methods, we present one algorithm that requires both functions to be smooth with Lipschitz continuous gradients and one algorithm that needs only one of the functions to be so. Algorithms in this paper are Gauss-Seidel type methods, in contrast to the ones proposed by Goldfarb and Ma in (Fast multiple splitting algorithms for convex optimization, Columbia University, 2009) where the algorithms are Jacobi type methods. Numerical results are reported to support our theoretical conclusions and demonstrate the practical potential of our algorithms.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据