block coordinate descent method – Page 2

Sparse Approximation via Penalty Decomposition Methods

Published: 2012/05/11, Updated: 2012/05/28

In this paper we consider sparse approximation problems, that is, general $l_0$ minimization problems with the $l_0$-“norm” of a vector being a part of constraints or objective function. In particular, we first study the first-order optimality conditions for these problems. We then propose penalty decomposition (PD) methods for solving them in which a sequence of … Read more

Row by row methods for semidefinite programming

Published: 2009/04/28

Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Nonlinear Optimization alternating direction method, block coordinate descent method, matrix completion, maximum cut, nonlinear gauss-seidel method, row by row method, semidefinite programming

We present a row-by-row (RBR) method for solving semidefinite programming (SDP) problem based on solving a sequence of problems obtained by restricting the n-dimensional positive semidefinite constraint on the matrix X. By fixing any (n-1)-dimensional principal submatrix of X and using its (generalized) Schur complement, the positive semidefinite constraint is reduced to a simple second-order … Read more