Skip to main content
Springer Nature Link
Log in

Adjustable robust counterpart of conic quadratic problems

  • Original Article
  • Published:
Mathematical Methods of Operations Research Aims and scope Submit manuscript

Abstract

This paper presents an approximate affinely adjustable robust counterpart for conic quadratic constraints. The theory is applied to obtain robust solutions to the problems of subway route design with implementation errors and a supply chain management with uncertain demands. Comparison of the adjustable solutions with the nominal and non-adjustable robust solutions shows that the adjustable (dynamic) robust solution maintains feasibility for all possible realizations, while being less conservative than the usual (static) robust counterpart solution.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Ben-Tal A, El Ghaoui L, Nemirovski A (2000) Robust semidefinite programming. In: Saigal R, Wolkowitcz H, Vandenberghe L(eds) Handbook on Semidefinite Programming. Kluwer, Dordrecht

    Google Scholar 

  • Ben-Tal A, Golany B, Nemirovski A, Vial J-Ph (2005) Supplier–retailer flexible commitment contracts: a robust optimization approach. Manuf Serv Oper Manage 7(3): 248–271

    Article  Google Scholar 

  • Ben-Tal A, Goryashko A, Guslitzer E, Nemirovski A (2004) Adjustable robust solutions of uncertain linear programs. Math Program 99(2): 351–376

    Article  MATH  MathSciNet  Google Scholar 

  • Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math Oper Res 23(4): 769–805

    Article  MATH  MathSciNet  Google Scholar 

  • Ben-Tal A, Nemirovski A (1999) Robust solutions to uncertain linear programs. OR Lett 25: 1–13

    MATH  MathSciNet  Google Scholar 

  • Ben-Tal A, Nemirovski A (2000) Robust solutions of linear programming problems contaminated with uncertain data. Math Program 88: 411–424

    Article  MATH  MathSciNet  Google Scholar 

  • Ben-Tal A, Nemirovski A (2002) Robust optimization methodology and applications. Math Program Ser B 92: 453–480

    Article  MATH  MathSciNet  Google Scholar 

  • Ben-Tal A, Nemirovski A, Roos C (2002) Robust solutions of uncertain quadratic and conic–quadratic problems. SIAM J Optim 13(12): 535–560

    Article  MATH  MathSciNet  Google Scholar 

  • Bertsimas D, Sim M (2006) Tractable approximations to robust conic optimization problems. Math Program 107(1): 5–36

    Article  MATH  MathSciNet  Google Scholar 

  • Boni O (2006) Robust Solutions of Conic Quadratic Problems. Research Thesis, Technion - Israel Institute of Technology. http://iew3.technion.ac.il/Labs/Opt/opt/Pap/odellia.pdf

  • Boni O, Ben-Tal A, Nemirovski A (2008) Robust solutions to conic quadratic problems. Optim Eng 9: 1–18

    Article  MathSciNet  Google Scholar 

  • El-Ghaoui L, Lebret H (1997) Robust solutions to least-square problems with uncertain data matrices. SIAM J Matrix Anal Appl 18(4): 1035–1064

    Article  MATH  MathSciNet  Google Scholar 

  • El-Ghaoui L, Oustry F, Lebret H (1998) Robust solutions to uncertain semidefinite programs. SIAM J Optim 9: 33–52

    Article  MATH  MathSciNet  Google Scholar 

  • Stürm J (1999) Using SeDuMi 1.02 a MATLAB toolbox for optimization over symmetric cones. Optim Methods Softw Res 11(12): 625–653

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. MINERVA Optimization Center, Faculty of Industrial Engineering and Management, Technion, Israel Institute of Technology, 32000, Technion city, Haifa, Israel

    Odellia Boni & Aharon Ben-Tal

Authors
  1. Odellia Boni
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Aharon Ben-Tal
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Odellia Boni.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Boni, O., Ben-Tal, A. Adjustable robust counterpart of conic quadratic problems. Math Meth Oper Res 68, 211–233 (2008). https://doi.org/10.1007/s00186-008-0218-9

Download citation

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00186-008-0218-9

Keywords