An Inexact Minimization Trust-Region Algorithm: Globalization of Newton's Method
El Hallabi, M.
In this work we define a trust region algorithm for approximating zeros of the overdetermined nonlinear system F(x) = 0, where F: R^n -> R^m is continuously differentiable. Instead of the l2 norm, arbitrary norms can be used in the objective function and in the trust region constraint. This research is an extension of El Hallabi and Tapia (1987) for nonlinear equations. We demonstrate that the algorithm under consideration is globally convergent. We also demonstrate that, under mild assumptions, the iteration sequence generated by this algorithm converges to a solution of the overdetermined system, and that it reduces after a finite number of steps to the Gauss-Newton iteration sequence.
Citable link to this pagehttps://hdl.handle.net/1911/101814
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