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 MFCGLS 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.

 
MFCGLS 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 MFCGLS, including data and scripts to reproduce all the tests described in the above paper. MFCGLS will be also included in IRtools, a MATLAB toolbox for iterative regularization of ill-posed linear systems, which will be released soon.