dc.contributor.author Ding, Lijun dc.date.accessioned 2022-01-24T18:07:45Z dc.date.available 2022-01-24T18:07:45Z dc.date.issued 2021-12 dc.identifier.other DING_cornellgrad_0058F_12784 dc.identifier.other http://dissertations.umi.com/cornellgrad:12784 dc.identifier.uri https://hdl.handle.net/1813/110818 dc.description 183 pages dc.description.abstract This thesis studies large scale semidefinite programming arising from modern applications. We first identify a set of regularity conditions, which we call simplicity, and show it holds in both a generic sense and in many practical applications. Next, based on simplicity, we derive conditioning results: error bounds and sensitivity of solution. Finally, we design an algorithm that is provably computationally efficient in terms of storage and time under simplicity. dc.description.abstract 这篇博士论文讨论现代应用中的大规模半正定规划。我们首先确认一组叫做质朴性的正则条件。质朴性条件不仅在某种一般意义下总是成立，而且也在特定的应用中成立。 接着，基于质朴性，我们推出一系列适定性结果：包括误差界和解的敏感性界。 最后，我们设计一个基于质朴性的算法。这个算法可被证明在时间和空间都是有效率的。 zh dc.language.iso en dc.rights Attribution 4.0 International dc.rights.uri https://creativecommons.org/licenses/by/4.0/ dc.title Large scale semidefinite programming: simplicity, conditioning, and an efficient algorithm dc.type dissertation or thesis thesis.degree.discipline Operations Research and Information Engineering thesis.degree.grantor Cornell University thesis.degree.level Doctor of Philosophy thesis.degree.name Ph. D., Operations Research and Information Engineering dc.contributor.chair Chen, Yudong dc.contributor.committeeMember Udell, Madeleine Richards dc.contributor.committeeMember Renegar, James dc.contributor.committeeMember Lewis, Adrian S. dcterms.license https://hdl.handle.net/1813/59810.2 dc.identifier.doi https://doi.org/10.7298/q16w-gg48
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