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dc.contributor.authorEl Hallabi, M.
Tapia, R.A.
dc.date.accessioned 2018-06-18T17:41:11Z
dc.date.available 2018-06-18T17:41:11Z
dc.date.issued 1993-09
dc.identifier.citation El Hallabi, M. and Tapia, R.A.. "A Global Convergence Theory for Arbitrary Norm Trust-Region Methods for Nonlinear Equations." (1993) https://hdl.handle.net/1911/101812.
dc.identifier.urihttps://hdl.handle.net/1911/101812
dc.description.abstract In this work we extend the Levenberg-Marquardt algorithm for approximating zeros of the nonlinear system F(x) = 0, where F : R^n -> R^n is continuously differentiable. Instead of the l2 norm, arbitrary norms can be used in the trust-region objective function and in the trust-region constraint. The algorithm is shown to be globally convergent. This research was motivated by the recent work of Duff, Nocedal and Reid. A key point in our analysis is that the tools from nonsmooth analysis and the Zangwill convergence theory allow us to establish essentially the same properties for an arbitrary norm trust-region algorithm that have been established for the Levenberg-Marquardt algorithm using the tools from smooth optimization. It is shown that all members of this class of algorithms locally reduce to Newton's method and that the iteration sequence actually converges to a solution.
dc.format.extent 21 pp
dc.title A Global Convergence Theory for Arbitrary Norm Trust-Region Methods for Nonlinear Equations
dc.type Technical report
dc.date.note September 1993 (Revised May 1995)
dc.identifier.digital TR93-41
dc.type.dcmi Text


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