A Levenberg-Marquardt method with approximate projections |
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Authors: | R. Behling A. Fischer M. Herrich A. Iusem Y. Ye |
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Affiliation: | 1. Department of Management Science and Engineering, Stanford University, Stanford, CA, 94305-4121, USA 2. Institute of Numerical Mathematics, Department of Mathematics, Technische Universit?t Dresden, 01062, Dresden, Germany 3. Instituto de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina 110, Rio de Janeiro, RJ, CEP 22460-320, Brazil
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Abstract: | The projected Levenberg-Marquardt method for the solution of a system of equations with convex constraints is known to converge locally quadratically to a possibly nonisolated solution if a certain error bound condition holds. This condition turns out to be quite strong since it implies that the solution sets of the constrained and of the unconstrained system are locally the same. Under a pair of more reasonable error bound conditions this paper proves R-linear convergence of a Levenberg-Marquardt method with approximate projections. In this way, computationally expensive projections can be avoided. The new method is also applicable if there are nonsmooth constraints having subgradients. Moreover, the projected Levenberg-Marquardt method is a special case of the new method and shares its R-linear convergence. |
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