Block Coordinate Descent Algorithms for Auxiliary-Function-Based Independent Vector Extraction

Efficient block-coordinate descent algorithms for the Group Lasso

We present two algorithms to solve the Group Lasso problem [33]. First, we propose a general version of the Block Coordinate Descent (BCD) algorithm for the Group Lasso that employs an efficient approach for optimizing each subproblem exactly. We show that it exhibits excellent performance when the groups are of moderate size. For groups of large size, we propose an extension of ISTA/FISTA [2] ...

Robust Block Coordinate Descent

In this paper we present a novel randomized block coordinate descent method for the minimization of a convex composite objective function. The method uses (approximate) partial second-order (curvature) information, so that the algorithm performance is more robust when applied to highly nonseparable or ill conditioned problems. We call the method Robust Coordinate Descent (RCD). At each iteratio...

Coordinate descent algorithms

Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity continues to grow because of their usefulness in data analysis, machine learning, and other areas of current interest. This paper describes the fundamentals of...

Block coordinate descent methods for semidefinite programming

Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework

We review algorithms developed for nonnegativematrix factorization (NMF) and 1 nonnegative tensor factorization (NTF) from a unified view based on the block coordinate 2 descent (BCD) framework. NMF and NTF are low-rank approximation methods for matri3 ces and tensors in which the low-rank factors are constrained to have only nonnegative 4 elements. The nonnegativity constraints have been shown...