Extending Scope of Robust Optimization: Comprehensive Robust Counterparts of Uncertain Problems

Authors:
Aharon Ben-Tal;Stephen Boyd;Arkadi Nemirovski
Affiliations:
Faculty of Industrial Engineering and Management, Technion – Israel Institute of Technology, 32000, Technion city, Haifa, Israel;Department of Electrical Engineering, Stanford University, Packard 264, 94305, Stanford, CA, USA;Faculty of Industrial Engineering and Management, Technion – Israel Institute of Technology, 32000, Technion city, Haifa, Israel
Venue:
Mathematical Programming: Series A and B
Year:
2006

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Abstract

In this paper, we propose a new methodology for handling optimization problems with uncertain data. With the usual Robust Optimization paradigm, one looks for the decisions ensuring a required performance for all realizations of the data from a given bounded uncertainty set, whereas with the proposed approach, we require also a controlled deterioration in performance when the data is outside the uncertainty set.The extension of Robust Optimization methodology developed in this paper opens up new possibilities to solve efficiently multi-stage finite-horizon uncertain optimization problems, in particular, to analyze and to synthesize linear controllers for discrete time dynamical systems.