Non-Negative Least Squares (NNLS) Module

Classes
class	Eigen::NNLS< MatrixType_ >
	Implementation of the Non-Negative Least Squares (NNLS) algorithm. More...

Detailed Description

This module provides a single class Eigen::NNLS implementing the NNLS algorithm. The algorithm is described in "SOLVING LEAST SQUARES PROBLEMS", by Charles L. Lawson and Richard J. Hanson, Prentice-Hall, 1974 and solves optimization problems of the form

$$min{\Vert Ax-b\Vert }_2^{2}s.t.x\ge 0.$$

The algorithm solves the constrained least-squares problem above by iteratively improving an estimate of which constraints are active (elements of $x$ equal to zero) and which constraints are inactive (elements of $x$ greater than zero). Each iteration, an unconstrained linear least-squares problem solves for the components of $x$ in the (estimated) inactive set and the sets are updated. The unconstrained problem minimizes ${\Vert A^N{x}^N-b\Vert }_2^2$, where $A^N$ is a matrix formed by selecting all columns of A which are in the inactive set $N$.