A Shamanskii-like Levenberg-Marquardt method for nonlinear equations

Jinyan Fan ()

Computational Optimization and Applications, 2013, vol. 56, issue 1, 63-80

Abstract: In this paper, we propose a Shamanskii-like Levenberg-Marquardt method for nonlinear equations. At every iteration, not only a LM step but also m−1 approximate LM steps are computed, where m is a positive integer. Under the local error bound condition which is weaker than nonsingularity, we show the Shamanskii-like LM method converges with Q-order m+1. The trust region technique is also introduced to guarantee the global convergence of the method. Since the Jacobian evaluation and matrix factorization are done after every m computations of the step, the overall cost of the Shamanskii-like LM method is usually much less than that of the general LM method (the m=1 case). Copyright Springer Science+Business Media New York 2013

Keywords: Nonlinear equations; Levenberg-Marquardt method; Local error bound condition (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10589-013-9549-4

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