Article

Mathematical Programming

, Volume 107, Issue 1, pp 63-89

First online:

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

  • Aharon Ben-TalAffiliated withFaculty of Industrial Engineering and Management, Technion – Israel Institute of Technology
  • , Stephen BoydAffiliated withDepartment of Electrical Engineering, Stanford University
  • , Arkadi NemirovskiAffiliated withFaculty of Industrial Engineering and Management, Technion – Israel Institute of Technology

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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.

Mathematics Subject Classification (2000)

90C05 90C25 90C34 93C05