  The coordinate descent (CD) method has recently become popular for solving
very large-scale problems, partly due to its simple update, low memory
requirement, and fast convergence. In this paper, we explore the greedy CD on
solving non-negative quadratic programming (NQP). The greedy CD generally has
much more expensive per-update complexity than its cyclic and randomized
counterparts. However, on the NQP, these three CDs have almost the same
per-update cost, while the greedy CD can have significantly faster overall
convergence speed. We also apply the proposed greedy CD as a subroutine to
solve linearly constrained NQP and the non-negative matrix factorization.
Promising numerical results on both problems are observed on instances with
synthetic data and also image data.
