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Abstract

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.