A hierarchy of policies for adaptive optimization

• Main Authors: Bertsimas, Dimitris J. (Contributor), Iancu, Dan Andrei (Author), Parrilo, Pablo A. (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor), Massachusetts Institute of Technology. Laboratory for Information and Decision Systems (Contributor), Massachusetts Institute of Technology. Operations Research Center (Contributor), Sloan School of Management (Contributor)
• Format: Article
• Language: English
• Published: Institute of Electrical and Electronics Engineers (IEEE), 2012-11-08T17:54:54Z.
• Subjects: Article
• Online Access: Get fulltext

 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.