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January  2013, 9(1): 227-241. doi: 10.3934/jimo.2013.9.227

## On the Levenberg-Marquardt methods for convex constrained nonlinear equations

 1 Department of Mathematics, and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, China

Received  January 2012 Revised  July 2012 Published  December 2012

In this paper, both the constrained Levenberg-Marquardt method and the projected Levenberg-Marquardt method are presented for nonlinear equations $F(x)=0$ subject to $x\in X$, where $X$ is a nonempty closed convex set. The Levenberg-Marquardt parameter is taken as $\| F(x_k) \|_2^\delta$ with $\delta\in (0, 2]$. Under the local error bound condition which is weaker than nonsingularity, the methods are shown to have the same convergence rate, which includes not only the convergence results obtained in [12] for $\delta=2$ but also the results given in [7] for unconstrained nonlinear equations.
Citation: Jinyan Fan. On the Levenberg-Marquardt methods for convex constrained nonlinear equations. Journal of Industrial & Management Optimization, 2013, 9 (1) : 227-241. doi: 10.3934/jimo.2013.9.227
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##### References:
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