A Levenberg-Marquardt method for large-scale bound-constrained nonlinear least-squares

• Main Author: Shan, Shidong
• Format: Others
• Language: English
• Published: University of British Columbia 2009
• Online Access: http://hdl.handle.net/2429/5648

The well known Levenberg-Marquardt method is used extensively for solving nonlinear least-squares problems. We describe an extension of the Levenberg- Marquardt method to problems with bound constraints on the variables. Each iteration of our algorithm approximately solves a linear least-squares problem subject to the original bound constraints. Our approach is especially suited to large-scale problems whose functions are expensive to compute; only matrix-vector products with the Jacobian are required. We present the results of numerical experiments that illustrate the effectiveness of the approach. Moreover, we describe its application to a practical curve fitting problem in fluorescence optical imaging.