- Separable Approximations and Decomposition Methods for the Augmented Lagrangian Rachael Tappenden( R.Tappendened.ac.uk ) Peter Richtarik(peter.richtariked.ac.uk) Burak Buke(b.bukeed.ac.uk) 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\'{a}rik and Tak\'{a}\v{c}. We show that the two methods are equivalent for feasibility problems up to the selection of a single step-size parameter. Furthermore, we prove an improved complexity bound for PCDM under strong convexity, and show that this bound is at least $8(L'/\bar{L})(\omega-1)^2$ 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. Keywords: augmented Lagrangian, decomposition, diagonal quadratic approximation, DQA, expected separable overapproximation, ESO, parallel coordinate descent method, PCDM, convex optimization, parallel computing Category 1: Convex and Nonsmooth Optimization (Convex Optimization ) Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization ) Category 3: Stochastic Programming Citation: Download: [PDF]Entry Submitted: 08/30/2013Entry Accepted: 08/30/2013Entry Last Modified: 08/30/2013Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.