Nonconvex robust optimization

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Operations Research Center.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2007

Author dc:creator

• Teo, Kwong Meng

Advisor dc:contributor.advisor

• Dimitris J. Bertsimas.

• Operations Research Center.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/40303

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/40303