A hierarchy of policies for adaptive optimization
In this paper, we propose a new tractable framework for dealing with linear dynamical systems affected by uncertainty, applicable to multistage robust optimization and stochastic programming. We introduce a hierarchy of near-optimal polynomial disturbance-feedback control policies, and show how thes...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Institute of Electrical and Electronics Engineers (IEEE)
2012
|
| Online Access: | http://hdl.handle.net/1721.1/74604 https://orcid.org/0000-0002-1985-1003 https://orcid.org/0000-0003-1132-8477 |
| _version_ | 1826214298527989760 |
|---|---|
| author | Iancu, Dan Andrei Parrilo, Pablo A. Bertsimas, Dimitris J |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Iancu, Dan Andrei Parrilo, Pablo A. Bertsimas, Dimitris J |
| author_sort | Iancu, Dan Andrei |
| collection | MIT |
| description | In this paper, we propose a new tractable framework for dealing with linear dynamical systems affected by uncertainty, applicable to multistage robust optimization and stochastic programming. We introduce a hierarchy of near-optimal polynomial disturbance-feedback control policies, and show how these can be computed by solving a single semidefinite programming problem. The approach yields a hierarchy parameterized by a single variable (the degree of the polynomial policies), which controls the trade-off between the optimality gap and the computational requirements. We evaluate our framework in the context of three classical applications-two in inventory management, and one in robust regulation of an active suspension system-in which very strong numerical performance is exhibited, at relatively modest computational expense. |
| first_indexed | 2024-09-23T16:03:20Z |
| format | Article |
| id | mit-1721.1/74604 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:03:20Z |
| publishDate | 2012 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/746042023-03-01T02:06:44Z A hierarchy of policies for adaptive optimization A Hierarchy of Near-Optimal Policies for Multistage Adaptive Optimization Iancu, Dan Andrei Parrilo, Pablo A. Bertsimas, Dimitris J Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Massachusetts Institute of Technology. Operations Research Center Sloan School of Management Bertsimas, Dimitris J. Parrilo, Pablo A. In this paper, we propose a new tractable framework for dealing with linear dynamical systems affected by uncertainty, applicable to multistage robust optimization and stochastic programming. We introduce a hierarchy of near-optimal polynomial disturbance-feedback control policies, and show how these can be computed by solving a single semidefinite programming problem. The approach yields a hierarchy parameterized by a single variable (the degree of the polynomial policies), which controls the trade-off between the optimality gap and the computational requirements. We evaluate our framework in the context of three classical applications-two in inventory management, and one in robust regulation of an active suspension system-in which very strong numerical performance is exhibited, at relatively modest computational expense. National Science Foundation (U.S.) (Grant EFRI-0735905) National Science Foundation (U.S.) (Grant DMI-0556106) United States. Air Force Office of Scientific Research (Grant FA9550-06-1-0303) 2012-11-08T17:54:54Z 2012-11-08T17:54:54Z 2011-08 2010-04 Article http://purl.org/eprint/type/JournalArticle 0018-9286 1558-2523 http://hdl.handle.net/1721.1/74604 Bertsimas, Dimitris, Dan Andrei Iancu, and Pablo A. Parrilo. “A Hierarchy of Near-Optimal Policies for Multistage Adaptive Optimization.” IEEE Transactions on Automatic Control 56.12 (2011): 2809–2824. https://orcid.org/0000-0002-1985-1003 https://orcid.org/0000-0003-1132-8477 en_US http://dx.doi.org/ 10.1109/TAC.2011.2162878 IEEE Transactions on Automatic Control Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) MIT web domain |
| spellingShingle | Iancu, Dan Andrei Parrilo, Pablo A. Bertsimas, Dimitris J A hierarchy of policies for adaptive optimization |
| title | A hierarchy of policies for adaptive optimization |
| title_full | A hierarchy of policies for adaptive optimization |
| title_fullStr | A hierarchy of policies for adaptive optimization |
| title_full_unstemmed | A hierarchy of policies for adaptive optimization |
| title_short | A hierarchy of policies for adaptive optimization |
| title_sort | hierarchy of policies for adaptive optimization |
| url | http://hdl.handle.net/1721.1/74604 https://orcid.org/0000-0002-1985-1003 https://orcid.org/0000-0003-1132-8477 |
| work_keys_str_mv | AT iancudanandrei ahierarchyofpoliciesforadaptiveoptimization AT parrilopabloa ahierarchyofpoliciesforadaptiveoptimization AT bertsimasdimitrisj ahierarchyofpoliciesforadaptiveoptimization AT iancudanandrei ahierarchyofnearoptimalpoliciesformultistageadaptiveoptimization AT parrilopabloa ahierarchyofnearoptimalpoliciesformultistageadaptiveoptimization AT bertsimasdimitrisj ahierarchyofnearoptimalpoliciesformultistageadaptiveoptimization AT iancudanandrei hierarchyofpoliciesforadaptiveoptimization AT parrilopabloa hierarchyofpoliciesforadaptiveoptimization AT bertsimasdimitrisj hierarchyofpoliciesforadaptiveoptimization |