The behavior of Newton's method on two equivalent systems from linear and nonlinear programming

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dc.contributor.advisorTapia, Richard A.en_US
dc.creatorVillalobos, Maria Cristinaen_US
dc.date.accessioned2009-06-04T08:12:13Zen_US
dc.date.available2009-06-04T08:12:13Zen_US
dc.date.issued2000en_US
dc.description.abstractNewton's method is a fundamental technique for approximating solutions of nonlinear equations. However, it is often not fully appreciated that the method can produce significantly different behavior when applied to equivalent systems. In this thesis, we investigate differences in local and global behavior of two well-known methods for constrained optimization: the Newton logarithmic barrier function method and the Newton primal-dual interior-point method. As we shall show, these two methods can be viewed as applying Newton's method to two different but equivalent systems. Through theoretical analysis and numerical experimentation, we show the Newton primal-dual method performs more effectively.en_US
dc.format.extent93 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH.SCI. 2000 VILLALOBOSen_US
dc.identifier.citationVillalobos, Maria Cristina. "The behavior of Newton's method on two equivalent systems from linear and nonlinear programming." (2000) Diss., Rice University. <a href="https://hdl.handle.net/1911/19563">https://hdl.handle.net/1911/19563</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/19563en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectMathematicsen_US
dc.titleThe behavior of Newton's method on two equivalent systems from linear and nonlinear programmingen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematical Sciencesen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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