Enforcing nonnegativity by flexible Krylov subspaces

A new fast solver, based on a flexible Krylov method, for nonnegative least squares problems

Constrained least squares problems arise in a variety of applications, and many iterative methods are already available to compute their solutions. This page is devoted to the presentation of a new solver for nonnegatively constrained least squares problems, dubbed

NNFCGLS (NonNegative Flexible CGLS) method.

The starting points for NNFCGLS are the Karush-Kuhn-Tucker (KKT) conditions, expressed for the least squares problem with nonnegativity constraints. The KKT conditions are leveraged to form an adaptively preconditioned linear system, which is then solved by a modified flexible conjugate gradient method.

NNFCGLS is described in details in the following paper:
FAST NONNEGATIVE LEAST SQUARES THROUGH FLEXIBLE KRYLOV SUBSPACES (draft),
which I coauthored with Yves Wiaux, and which is published in the SIAM Journal of Scientific Computing, 39(2), A655--A679 (2017)

Click here to download a MATLAB software implementing NNFCGLS, including data and scripts to reproduce all the tests described in the above paper. NNFCGLS will be also included in IR Tools, a MATLAB toolbox for iterative regularization of ill-posed linear systems, which will be released soon.