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Zbl 1075.65075
Gould, Nicholas I.M.; Leyffer, Sven; Toint, Philippe L.
A multidimensional filter algorithm for nonlinear equations and nonlinear least-squares. (English)
[J] SIAM J. Optim. 15, No. 1, 17-38 (2004). ISSN 1052-6234; ISSN 1095-7189/e

Summary: We introduce a new algorithm for the solution of systems of nonlinear equations and nonlinear least-squares problems that attempts to combine the efficiency of filter techniques and the robustness of trust-region methods. The algorithm is shown, under reasonable assumptions, to globally converge to zeros of the system, or to first-order stationary points of the Euclidean norm of its residual. Preliminary numerical experience is presented that shows substantial gains in efficiency over the traditional monotone trust-region approach.

MSC 2000:: *65H10 Systems of nonlinear equations (numerical methods)
65K05 Mathematical programming (numerical methods)
90C30 Nonlinear programming
90C06 Large-scale problems

Keywords: nonlinear equations; nonlinear least-squares; nonlinear fitting; filter methods; trust-region algorithms; global convergence; numerical examples

Cited in: Zbl 1122.90074

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