A global optimization technique for zero-residual nonlinear least-squares problems

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dc.contributor.advisorTapia, Richard A.en_US
dc.creatorVelazquez Martinez, Leticiaen_US
dc.date.accessioned2009-06-04T06:59:27Zen_US
dc.date.available2009-06-04T06:59:27Zen_US
dc.date.issued2000en_US
dc.description.abstractThis thesis introduces a globalization strategy for approximating global minima of zero-residual least-squares problems. This class of nonlinear programming problems arises often in data-fitting applications in the fields of engineering and applied science. Such minimization problems are formulated as a sum of squares of the errors between the calculated and observed values. In a zero-residual problem at a global solution, the calculated values from the model matches exactly the known data. The presence of multiple local minima is the main difficulty. Algorithms tend to get trapped at local solutions when applied to these problems. The proposed algorithm is a combination of a simple random sampling, a Levenberg-Marquardt-type method, a scaling technique, and a unit steplength. The key component of the algorithm is that a unit steplength is used. An interesting consequence is that this approach is not attracted to non-degenerate saddle points or to large-residual local minima. Numerical experiments are conducted on a set of zero-residual problems, and the numerical results show that the new multi-start strategy is relatively more effective and robust than some other global optimization algorithms.en_US
dc.format.extent70 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH.SCI. 2000 VELAZQUEZ MARTINEZen_US
dc.identifier.citationVelazquez Martinez, Leticia. "A global optimization technique for zero-residual nonlinear least-squares problems." (2000) Diss., Rice University. <a href="https://hdl.handle.net/1911/19533">https://hdl.handle.net/1911/19533</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/19533en_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.titleA global optimization technique for zero-residual nonlinear least-squares problemsen_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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