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On the convergence of an inexact Gauss-Newton trust-region method for nonlinear least-squares problems with simple bounds

Margherita Porcelli (porcelli***at***math.unifi.it)

Abstract: We introduce an inexact Gauss-Newton trust-region method for solving bound-constrained nonlinear least-squares problems where, at each iteration, a trust-region subproblem is approximately solved by the Conjugate Gradient method. Provided a suitable control on the accuracy to which we attempt to solve the subproblems, we prove that the method has global and asymptotic fast convergence properties.

Keywords: bound-constrained nonlinear least-squares, simple bounds, trust-region methods, convergence theory, affine scaling

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Bound-constrained Optimization )

Category 3: Nonlinear Optimization (Nonlinear Systems and Least-Squares )

Citation: M.Porcelli, "On the convergence of an inexact Gauss-Newton trust-region method for nonlinear least-squares problems with simple bounds", Optimization Letters, 7:3 (2013), pp. 447–-465. DOI:10.1007/s11590-011-0430-z

Download: [PDF]

Entry Submitted: 02/24/2011
Entry Accepted: 02/24/2011
Entry Last Modified: 11/09/2013

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