The numerical algebraic geometry approach to polynomial optimization
| dc.contributor.author | Davis, Brent R., author | |
| dc.contributor.author | Bates, Daniel J., advisor | |
| dc.contributor.author | Peterson, Chris, advisor | |
| dc.contributor.author | Kirby, Michael, committee member | |
| dc.contributor.author | Maciejewski, A. A., committee member | |
| dc.date.accessioned | 2017-09-14T16:05:52Z | |
| dc.date.available | 2017-09-14T16:05:52Z | |
| dc.date.issued | 2017 | |
| dc.description.abstract | Numerical algebraic geometry (NAG) consists of a collection of numerical algorithms, based on homotopy continuation, to approximate the solution sets of systems of polynomial equations arising from applications in science and engineering. This research focused on finding global solutions to constrained polynomial optimization problems of moderate size using NAG methods. The benefit of employing a NAG approach to nonlinear optimization problems is that every critical point of the objective function is obtained with probability-one. The NAG approach to global optimization aims to reduce computational complexity during path tracking by exploiting structure that arises from the corresponding polynomial systems. This thesis will consider applications to systems biology and life sciences where polynomials solve problems in model compatibility, model selection, and parameter estimation. Furthermore, these techniques produce mathematical models of large data sets on non-euclidean manifolds such as a disjoint union of Grassmannians. These methods will also play a role in analyzing the performance of existing local methods for solving polynomial optimization problems. | |
| dc.format.medium | born digital | |
| dc.format.medium | doctoral dissertations | |
| dc.identifier | Davis_colostate_0053A_14362.pdf | |
| dc.identifier.uri | https://hdl.handle.net/10217/183991 | |
| dc.language | English | |
| dc.language.iso | eng | |
| dc.publisher | Colorado State University. Libraries | |
| dc.relation.ispartof | 2000-2019 | |
| dc.rights | Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright. | |
| dc.subject | application | |
| dc.subject | homotopy | |
| dc.subject | optimization | |
| dc.subject | geometry | |
| dc.subject | algebraic | |
| dc.subject | numerical | |
| dc.title | The numerical algebraic geometry approach to polynomial optimization | |
| dc.type | Text | |
| dcterms.rights.dpla | This Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). | |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | Colorado State University | |
| thesis.degree.level | Doctoral | |
| thesis.degree.name | Doctor of Philosophy (Ph.D.) |
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