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Partly Smooth Models and Algorithms

dc.contributor.authorWylie, Calvin
dc.contributor.chairLewis, Adrian S.
dc.contributor.committeeMemberDavis, Damek Shea
dc.contributor.committeeMemberBindel, David S.
dc.date.accessioned2020-06-23T18:02:39Z
dc.date.available2020-06-23T18:02:39Z
dc.date.issued2019-12
dc.description126 pages
dc.description.abstractOptimization 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.doihttps://doi.org/10.7298/c7gg-3e23
dc.identifier.otherWylie_cornellgrad_0058F_11824
dc.identifier.otherhttp://dissertations.umi.com/cornellgrad:11824
dc.identifier.urihttps://hdl.handle.net/1813/70089
dc.language.isoen
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.titlePartly Smooth Models and Algorithms
dc.typedissertation or thesis
dcterms.licensehttps://hdl.handle.net/1813/59810
thesis.degree.disciplineOperations Research and Information Engineering
thesis.degree.levelDoctor of Philosophy
thesis.degree.namePh. D., Operations Research and Information Engineering

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