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Abstract
In this paper we study decomposition methods based on separable approximations for minimizing the augmented Lagrangian. In particular, we study and compare the Diagonal Quadratic Approximation Method (DQAM) of Mulvey and Ruszczy\'{n}ski and the Parallel Coordinate Descent Method (PCDM) of Richt\'arik and Tak\'a\v{c}. We show that the two methods are equivalent for feasibility problems up to the selection of a single stepsize parameter. Furthermore, we prove an improved complexity bound for PCDM under strong convexity, and show that this bound is at least $8(L'/\bar{L})(\omega1)^2$ times better than the best known bound for DQAM, where $\omega$ is the degree of partial separability and $L'$ and $\bar{L}$ are the maximum and average of the block Lipschitz constants of the gradient of the quadratic penalty appearing in the augmented Lagrangian.
Original language  English 

Publisher  ArXiv 
Publication status  Published  30 Aug 2013 
Keywords
 math.OC
 cs.DC
 cs.NA
 stat.ML
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Projects
 1 Finished

Science and Innovation: Numerical Algorithms and Intelligent Software for the Evolving HPC Platform
1/08/09 → 31/07/14
Project: Research
Research output
 1 Article

Separable approximations and decomposition methods for the augmented Lagrangian
Tappenden, R., Richtarik, P. & Buke, B., 6 Nov 2014, In: Optimization Methods and Software. 30, 3, p. 643668Research output: Contribution to journal › Article › peerreview
Open AccessFile