NII Technical Report (NII-2016-001E)

Title Modulus-Type Inner Outer Iteration Methods for Nonnegative Constrained Least Squares Problems (Revised Version)
Authors Ning Zheng, Ken Hayami, and Jun-Feng Yin
Abstract For the solution of large sparse nonnegative constrained least squares (NNLS) problems, a new iterative method is proposed which uses the CGLS method for the inner iterations and the modulus iterative method for the outer iterations to solve the linear complementarity problem resulting from the Karush-Kuhn-Tucker condition of the NNLS problem. Theoretical convergence analysis including the optimal choice of the parameter matrix is presented for the proposed method. In addition, the method can be further enhanced by incorporating the active set strategy, which contains two stages where the first stage consists of modulus iterations to identify the active set, while the second stage solves the reduced unconstrained least squares problems only on the inactive variables, and projects the solution into the nonnegative region. Numerical experiments show the efficiency of the proposed methods compared to projection gradient-type methods with less iteration steps and CPU time.
Language English
Published Jan 12, 2016
Pages 29p
PDF File 16-001E.pdf

NII Technical Reports
National Institute of Informatics