Adaptable optimization : theory and algorithms

Optimization under uncertainty is a central ingredient for analyzing and designing systems with incomplete information. This thesis addresses uncertainty in optimization, in a dynamic framework where information is revealed sequentially, and future decisions are adaptable, i.e., they depend functionally on the information revealed in the past. Such problems arise in applications where actions are repeated over a time horizon (e.g., portfolio management, or dynamic scheduling problems), or that have multiple planning stages (e.g., network design). The first part of the thesis focuses on the robust optimization approach to systems with uncertainty. Unlike the probability-driven stochastic programming approach, robust optimization is built on deterministic set-based formulations of uncertainty. This thesis seeks to place Robust Optimization within a dynamic framework. In particular, we introduce the notion of finite adaptability. Using geometric results, we characterize the benefits of adaptability, and use these theoretical results to design efficient algorithms for finding near-optimal protocols. Among the novel contributions of the work are the capacity to accommodate discrete variables, and the development of a hierarchy of adaptability.

Department dc:contributor.department

Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2006

Author dc:creator

• Caramanis, Constantine (Constantine Michael), 1977-

Advisor dc:contributor.advisor

• Dimitris J. Bertsimas.

• Electrical Engineering and Computer Science.

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/1721.1/38301

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/38301