Mathematical Programming

, Volume 107, Issue 1, pp 63–89

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

  • Aharon Ben-Tal
  • Stephen Boyd
  • Arkadi Nemirovski

DOI: 10.1007/s10107-005-0679-z

Cite this article as:
Ben-Tal, A., Boyd, S. & Nemirovski, A. Math. Program. (2006) 107: 63. doi:10.1007/s10107-005-0679-z


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.

Mathematics Subject Classification (2000)

90C05 90C25 90C34 93C05 

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Aharon Ben-Tal
    • 1
  • Stephen Boyd
    • 2
  • Arkadi Nemirovski
    • 1
  1. 1.Faculty of Industrial Engineering and ManagementTechnion – Israel Institute of TechnologyTechnion cityIsrael
  2. 2.Department of Electrical EngineeringStanford UniversityStanfordUSA

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