Partly Smooth Models and Algorithms
| dc.contributor.author | Wylie, Calvin | |
| dc.contributor.chair | Lewis, Adrian S. | |
| dc.contributor.committeeMember | Davis, Damek Shea | |
| dc.contributor.committeeMember | Bindel, David S. | |
| dc.date.accessioned | 2020-06-23T18:02:39Z | |
| dc.date.available | 2020-06-23T18:02:39Z | |
| dc.date.issued | 2019-12 | |
| dc.description | 126 pages | |
| dc.description.abstract | Optimization and variational problems typically involve a highly structured blend of smooth and nonsmooth geometry. In nonlinear programming, such structure underlies the design of active-set algorithms, in which a globally convergent process first simplifies the problem by identifying active constraints at the solution; a second phase then employs a rapidly-convergent Newton-type method, with linear models of the simplified problem playing a central role. The theory of partial smoothness formalizes and highlights the fundamental geometry driving ``identification.'' This dissertation concentrates on the second phase, and understanding accelerated local convergence in partly smooth settings. A key contribution is a simple algorithm for ``black-box'' nonsmooth optimization, that incorporates second-order information with the usual linear approximation oracle. Motivated by active sets and sequential quadratic programming, a model-based approach is used to prove local quadratic convergence for a broad class of objectives. Promising numerical results on more general functions, as well as simple first-order analogues, are discussed. Beyond optimization, an intuitive linearization scheme for generalized equations is formalized, with simple techniques based on classical differential geometry: manifolds, normal and tangent spaces, and constant rank maps. The approach illuminates fundamental geometric ideas behind active-set acceleration techniques for variational inequalities, as well as second-order theory and algorithms for structured nonsmooth optimization. | |
| dc.identifier.doi | https://doi.org/10.7298/c7gg-3e23 | |
| dc.identifier.other | Wylie_cornellgrad_0058F_11824 | |
| dc.identifier.other | http://dissertations.umi.com/cornellgrad:11824 | |
| dc.identifier.uri | https://hdl.handle.net/1813/70089 | |
| dc.language.iso | en | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.title | Partly Smooth Models and Algorithms | |
| dc.type | dissertation or thesis | |
| dcterms.license | https://hdl.handle.net/1813/59810 | |
| thesis.degree.discipline | Operations Research and Information Engineering | |
| thesis.degree.level | Doctor of Philosophy | |
| thesis.degree.name | Ph. D., Operations Research and Information Engineering |
Files
Original bundle
1 - 1 of 1
Loading...
- Name:
- Wylie_cornellgrad_0058F_11824.pdf
- Size:
- 4.13 MB
- Format:
- Adobe Portable Document Format