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|Title:||A block coordinate gradient descent method for regularized convex separable optimization and covariance selection||Authors:||Yun, S.
Block coordinate gradient descent
Linear rate convergence
Maximum likelihood estimation
|Issue Date:||Oct-2011||Citation:||Yun, S., Tseng, P., Toh, K.-C. (2011-10). A block coordinate gradient descent method for regularized convex separable optimization and covariance selection. Mathematical Programming 129 (2) : 331-355. ScholarBank@NUS Repository. https://doi.org/10.1007/s10107-011-0471-1||Abstract:||We consider a class of unconstrained nonsmooth convex optimization problems, in which the objective function is the sum of a convex smooth function on an open subset of matrices and a separable convex function on a set of matrices. This problem includes the covariance selection problem that can be expressed as an ℓ1-penalized maximum likelihood estimation problem. In this paper, we propose a block coordinate gradient descent method (abbreviated asBCGD)for solving this class of nonsmooth separable problems with the coordinate block chosen by a Gauss-Seidel rule. The method is simple, highly parallelizable, and suited for large-scale problems. We establish global convergence and, under a local Lipschizian error bound assumption, linear rate of convergence for this method. For the covariance selection problem, the method can terminate in O(n3/ε) iterations with an ε-optimal solution. We compare the performance of the BCGD method with the first-order methods proposed by Lu (SIAM J Optim 19:1807-1827, 2009; SIAM J Matrix Anal Appl 31:2000-2016, 2010) for solving the covariance selection problem on randomly generated instances. Our numerical experience suggests that the BCGD method can be efficient for largescale covariance selection problems with constraints. © Springer and Mathematical Optimization Society 2011.||Source Title:||Mathematical Programming||URI:||http://scholarbank.nus.edu.sg/handle/10635/102605||ISSN:||00255610||DOI:||10.1007/s10107-011-0471-1|
|Appears in Collections:||Staff Publications|
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