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dc.creatorEL HALLABI, MOHAMMEDI
dc.date.accessioned 2007-05-09T19:44:15Z
dc.date.available 2007-05-09T19:44:15Z
dc.date.issued 1987
dc.identifier.urihttps://hdl.handle.net/1911/16051
dc.description.abstract In this research we extend the Levenberg-Marquardt algorithm for approximating zeros of the nonlinear system F(x) = 0, where F is continuously differentiable from ${\rm I\!R}\sp{n}$ to ${\rm I\!R}\sp{n}.$ Instead of the $l\sb 2$-norm, arbitrary norms can be used in the 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, namely locally Lipschitz analysis, allow us to establish essentially the same properties for our algorithm that have been established for the Levenberg-Marquardt algorithm using the tools from smooth optimization. In our analysis, the sequence generated by the algorithm is the couple $(x\sb{k},\delta\sb{k})$ where $x\sb{k}$ is the iterate and $\delta\sb{k}$ the trust region radius. Since the successor $(x\sb{k+1},\delta\sb{k+1})$ of $(x\sb{k},\delta\sb{k})$ is not unique we model our algorithm by a point-to-set map and then apply Zangwill's theorem of convergence to our case. It is shown that our algorithm reduces locally to Newton's method.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.subjectMathematics
dc.title A GLOBAL CONVERGENCE THEORY FOR ARBITRARY NORM TRUST REGION METHODS FOR NONLINEAR EQUATIONS
dc.type.genre Thesis
dc.type.material Text
thesis.degree.department Mathematics
thesis.degree.discipline Natural Sciences
thesis.degree.grantor Rice University
thesis.degree.level Doctoral
thesis.degree.name Doctor of Philosophy
dc.identifier.citation EL HALLABI, MOHAMMEDI. "A GLOBAL CONVERGENCE THEORY FOR ARBITRARY NORM TRUST REGION METHODS FOR NONLINEAR EQUATIONS." (1987) Diss., Rice University. https://hdl.handle.net/1911/16051.


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