Sangwoon Yun The affine rank minimization problem, which consists of finding a matrix of minimum rank subject to linear equality constraints, has been proposed in many areas of engineering and science. A specific rank minimization problem is the matrix completion problem, in which we wish to recover a (low-rank) data matrix from incomplete samples of its entries. … Read more
In applications such as signal processing and statistics, many problems involve finding sparse solutions to under-determined linear systems of equations. These problems can be formulated as a structured nonsmooth optimization problems, i.e., the problem of minimizing L_1-regularized linear least squares problems. In this paper, we propose a block coordinate gradient descent method (abbreviated as CGD) … Read more
Support vector machines (SVMs) training may be posed as a large quadratic program (QP) with bound constraints and a single linear equality constraint. We propose a (block) coordinate gradient descent method for solving this problem and, more generally, linearly constrained smooth optimization. Our method is closely related to decomposition methods currently popular for SVM training. … Read more
We consider the problem of minimizing the sum of a smooth function and a separable convex function. This problem includes as special cases bound-constrained optimization and smooth optimization with l_1-regularization. We propose a (block) coordinate gradient descent method for solving this class of nonsmooth separable problems. We establish global convergence and, under a local Lipschitzian … Read more