# NNLS

##### Kim-Chuan Toh, Sangwoon Yun

The software was first released on 14 Oct 2009. It was last updated in 10 Nov 2009 with some minor bugs corrected. The software is designed to solve nuclear norm regularized linear least squares problems of the form:

$$\begin{eqnarray*}&\min&\Big\{ f(X)+\mu\|X\|_* \mid X \in \mathbb{R}^{m\times n} \Big\} \\[5pt] &\min&\Big\{ f(X)+\mu Tr(X) \mid X \in \mathbb{S}^{n}_+ \Big\} \end{eqnarray*}$$

where $$\mu > 0$$ is a regularization parameter, and $$f(X) = \frac{1}{2}\|{\cal A}(X)-b\|^2$$.

Important note: this is a research software. It is not intended nor designed to be a general purpose software at the moment. The solver is expected to work well only for favorable problems such as nuclear norm regularized random matrix completion problems. Being a gradient method, it is quite sensitive to the various parameters used in the algorithm. The selection of the parameters typically depend on the class of problems being solved.

Citation: Kim-Chuan Toh and Sangwoon Yun, An accelerated proximal gradient algorithm for nuclear norm regularized least squares problems, Pacific J. Optimization, 6 (2010), pp. 615–640.