Risk and robust optimization
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2008
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| Online Access: | http://dspace.mit.edu/handle/1721.1/37894 http://hdl.handle.net/1721.1/37894 |
| _version_ | 1826211243908661248 |
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| author | Brown, David Benjamin, Ph. D. Massachusetts Institute of Technology |
| author2 | Dimitris J. Bertsimas. |
| author_facet | Dimitris J. Bertsimas. Brown, David Benjamin, Ph. D. Massachusetts Institute of Technology |
| author_sort | Brown, David Benjamin, Ph. D. Massachusetts Institute of Technology |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006. |
| first_indexed | 2024-09-23T15:03:10Z |
| format | Thesis |
| id | mit-1721.1/37894 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T15:03:10Z |
| publishDate | 2008 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/378942019-04-10T12:50:38Z Risk and robust optimization Brown, David Benjamin, Ph. D. Massachusetts Institute of Technology Dimitris J. Bertsimas. Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. Electrical Engineering and Computer Science. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006. Includes bibliographical references (p. 203-213). This thesis develops and explores the connections between risk theory and robust optimization. Specifically, we show that there is a one-to-one correspondence between a class of risk measures known as coherent risk measures and uncertainty sets in robust optimization. An important consequence of this is that one may construct uncertainty sets, which are the critical primitives of robust optimization, using decision-maker risk preferences. In addition, we show some results on the geometry of such uncertainty sets. We also consider a more general class of risk measures known as convex risk measures, and show that these risk measures lead to a more flexible approach to robust optimization. In particular, these models allow one to specify not only the values of the uncertain parameters for which feasibility should be ensured, but also the degree of feasibility. We show that traditional, robust optimization models are a special case of this framework. As a result, this framework implies a family of probability guarantees on infeasibility at different levels, as opposed to standard, robust approaches which generally imply a single guarantee. (cont.) Furthermore, we illustrate the performance of these risk measures on a real-world portfolio optimization application and show promising results that our methodology can, in some cases, yield significant improvements in downside risk protection at little or no expense in expected performance over traditional methods. While we develop this framework for tile case of linear optimization under uncertainty, we show how to extend the results to optimization over more general cones. Moreover, our methodology is scenario-based, and( we prove a new rate of convergence result on a specific class of convex risk measures. Finally, we consider a multi-stage problem under uncertainty, specifically optimization of quadratic functions over un-certain linear systems. Although the theory of risk measures is still undeveloped with respect to dynamic optimization problems. we show that a set-based model of uncertainty yields a tractable approach to this problem in the presence of constraints. Moreover, we are able to derive a near-closed form solution for this approach and prove new probability guarantees on its resulting performance. by David Benjamin Brown. Ph.D. 2008-01-10T17:20:44Z 2008-01-10T17:20:44Z 2006 2006 Thesis http://dspace.mit.edu/handle/1721.1/37894 http://hdl.handle.net/1721.1/37894 132692470 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/37894 http://dspace.mit.edu/handle/1721.1/7582 213 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Electrical Engineering and Computer Science. Brown, David Benjamin, Ph. D. Massachusetts Institute of Technology Risk and robust optimization |
| title | Risk and robust optimization |
| title_full | Risk and robust optimization |
| title_fullStr | Risk and robust optimization |
| title_full_unstemmed | Risk and robust optimization |
| title_short | Risk and robust optimization |
| title_sort | risk and robust optimization |
| topic | Electrical Engineering and Computer Science. |
| url | http://dspace.mit.edu/handle/1721.1/37894 http://hdl.handle.net/1721.1/37894 |
| work_keys_str_mv | AT browndavidbenjaminphdmassachusettsinstituteoftechnology riskandrobustoptimization |