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dc.contributor.advisor Dennis, John E., Jr.
dc.contributor.advisor Tapia, Richard A.
dc.creatorMartinez R., Hector Jairo
dc.date.accessioned 2009-06-04T00:00:10Z
dc.date.available 2009-06-04T00:00:10Z
dc.date.issued 1988
dc.identifier.citation Martinez R., Hector Jairo. "Local and superlinear convergence of structured secant methods from the convex class." (1988) Diss., Rice University. https://hdl.handle.net/1911/16167.
dc.identifier.urihttps://hdl.handle.net/1911/16167
dc.description.abstract In this thesis we develop a unified theory for establishing the local and q-superlinear convergence of secant methods which use updates from Broyden's convex class and have been modified to take advantage of the structure present in the Hessian in constructing approximate Hessians. As an application of this theory, we show the local and q-superlinear convergence of any structured secant method which use updates from the convex class for the equality-constrained optimization problem and the nonlinear least-squares problem. Particular cases of these methods are the SQP augmented scale BFGS and DFP secant methods for constrained optimization problems introduced by Tapia. Another particular case, for which local and q-superlinear convergence is proved for the first time here, is the Al-Baali and Fletcher modification of the structured BFGS secant method considered by Dennis, Gay and Welsch for the nonlinear least-squares problem and implemented in the current version of the NL2SOL code.
dc.format.extent 58 p.
dc.format.mimetype application/pdf
dc.language.iso eng
dc.subjectMathematics
Computer science
Statistics
dc.title Local and superlinear convergence of structured secant methods from the convex class
dc.type.genre Thesis
dc.type.material Text
thesis.degree.department Statistics
thesis.degree.discipline Engineering
thesis.degree.grantor Rice University
thesis.degree.level Doctoral
thesis.degree.name Doctor of Philosophy


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