Large scale semidefinite programming: simplicity, conditioning, and an efficient algorithm
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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.
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。
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。
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183 pages
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2021-12
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Chen, Yudong
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Udell, Madeleine Richards
Renegar, James
Lewis, Adrian S.
Renegar, James
Lewis, Adrian S.
Degree Discipline
Operations Research and Information Engineering
Degree Name
Ph. D., Operations Research and Information Engineering
Degree Level
Doctor of Philosophy
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Attribution 4.0 International
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dissertation or thesis