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Kanzow, Christian; Yamashita, Nobuo; Fukushima, Masao

Levenberg–Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints. (English) Zbl 1064.65037

J. Comput. Appl. Math. 172, No. 2, 375-397 (2004).
Two Levenberg-Marquardt algorithms are considered for the solution of a, not necessarily square, system of nonlinear equations with convex constraints. Motivated by an earlier paper of N. Yamashita and M. Fukushima [Comput. Suppl. 15, 239–249 (2001; Zbl 1001.65047)] the usual nonsingularity assumption is replaced by an error bound condition that allows the solution set to be (locally) nonunique. At each step, one of the algorithms solves a strictly convex minimization problem, while the other requires only the solution of one system of linear equations. Both methods are shown to converge locally quadratically. Some numerical examples for the second method are given.
Reviewer: W. C. Rheinboldt (Pittsburgh)

Cited in 2 Reviews
Cited in 85 Documents

MSC:

65H10 Numerical computation of solutions to systems of equations
90C25 Convex programming

Keywords:

constraint equation; Levenberg-Marquardt method; projected gradient; quadratic convergence; error bounds; algorithm; convex minimization; numerical examples

Citations:

Zbl 1001.65047

Software:

STRSCNE; levmar
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\textit{C. Kanzow} et al., J. Comput. Appl. Math. 172, No. 2, 375--397 (2004; Zbl 1064.65037)
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