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Mathematical Programming

, Volume 92, Issue 3, pp 453–480 | Cite as

Robust optimization – methodology and applications

  • Aharon Ben-Tal
  • Arkadi Nemirovski

Abstract.

Robust Optimization (RO) is a modeling methodology, combined with computational tools, to process optimization problems in which the data are uncertain and is only known to belong to some uncertainty set. The paper surveys the main results of RO as applied to uncertain linear, conic quadratic and semidefinite programming. For these cases, computationally tractable robust counterparts of uncertain problems are explicitly obtained, or good approximations of these counterparts are proposed, making RO a useful tool for real-world applications. We discuss some of these applications, specifically: antenna design, truss topology design and stability analysis/synthesis in uncertain dynamic systems. We also describe a case study of 90 LPs from the NETLIB collection. The study reveals that the feasibility properties of the usual solutions of real world LPs can be severely affected by small perturbations of the data and that the RO methodology can be successfully used to overcome this phenomenon.

Key words: convex optimization – data uncertainty – robustness – linear programming – quadratic programming – semidefinite programming – engineering design – Lyapunov stability synthesis 
Mathematics Subject Classification (1991): 90C05, 90C25, 90C30 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Aharon Ben-Tal
    • 1
  • Arkadi Nemirovski
    • 1
  1. 1.Faculty of Industrial Engineering and Management, Technion – Israel Institute of Technology, Technion City, Haifa 32000, Israel e-mail: {morbt,nemirovs}@ie.technion.ac.ilIL

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