Nonconvex robust optimization
Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2007.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2008
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| Online Access: | http://hdl.handle.net/1721.1/40303 |
| _version_ | 1826203203414261760 |
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| author | Teo, Kwong Meng |
| author2 | Dimitris J. Bertsimas. |
| author_facet | Dimitris J. Bertsimas. Teo, Kwong Meng |
| author_sort | Teo, Kwong Meng |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2007. |
| first_indexed | 2024-09-23T12:32:56Z |
| format | Thesis |
| id | mit-1721.1/40303 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T12:32:56Z |
| publishDate | 2008 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/403032019-04-11T13:40:37Z Nonconvex robust optimization Teo, Kwong Meng Dimitris J. Bertsimas. Massachusetts Institute of Technology. Operations Research Center. Massachusetts Institute of Technology. Operations Research Center. Operations Research Center. Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2007. This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. Includes bibliographical references (p. 133-138). We propose a novel robust optimization technique, which is applicable to nonconvex and simulation-based problems. Robust optimization finds decisions with the best worst-case performance under uncertainty. If constraints are present, decisions should also be feasible under perturbations. In the real-world, many problems are nonconvex and involve computer-based simulations. In these applications, the relationship between decision and outcome is not defined through algebraic functions. Instead, that relationship is embedded within complex numerical models. Since current robust optimization methods are limited to explicitly given convex problems, they cannot be applied to many practical problems. Our proposed method, however, operates on arbitrary objective functions. Thus, it is generic and applicable to most real-world problems. It iteratively moves along descent directions for the robust problem, and terminates at a robust local minimum. Because the concepts of descent directions and local minima form the building blocks of powerful optimization techniques, our proposed framework shares the same potential, but for the richer, and more realistic, robust problem. (cont.) To admit additional considerations including parameter uncertainties and nonconvex constraints, we generalized the basic robust local search. In each case, only minor modifications are required - a testimony to the generic nature of the method, and its potential to be a component of future robust optimization techniques. We demonstrated the practicability of the robust local search technique in two realworld applications: nanophotonic design and Intensity Modulated Radiation Therapy (IMRT) for cancer treatment. In both cases, the numerical models are verified by actual experiments. The method significantly improved the robustness for both designs, showcasing the relevance of robust optimization to real-world problems. by Kwong Meng Teo. Ph.D. 2008-02-27T20:36:39Z 2008-02-27T20:36:39Z 2007 2007 Thesis http://hdl.handle.net/1721.1/40303 191109737 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/1721.1/7582 138 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Operations Research Center. Teo, Kwong Meng Nonconvex robust optimization |
| title | Nonconvex robust optimization |
| title_full | Nonconvex robust optimization |
| title_fullStr | Nonconvex robust optimization |
| title_full_unstemmed | Nonconvex robust optimization |
| title_short | Nonconvex robust optimization |
| title_sort | nonconvex robust optimization |
| topic | Operations Research Center. |
| url | http://hdl.handle.net/1721.1/40303 |
| work_keys_str_mv | AT teokwongmeng nonconvexrobustoptimization |