Abstract and Applied Analysis

Tractable Approximation to Robust Nonlinear Production Frontier Problem

Lei Wang, Xing Wang, and Nan-jing Huang

Full-text: Open access

Abstract

Robust optimization is a rapidly developing methodology for handling optimization problems affected by the uncertain-but-bounded data perturbations. In this paper, we consider the nonlinear production frontier problem where the traditional expected linear cost minimization objective is replaced by one that explicitly addresses cost variability. We propose a robust counterpart for the nonlinear production frontier problem that preserves the computational tractability of the nominal problem. We also provide a guarantee on the probability that the robust solution is feasible when the uncertain coefficients obey independent and identically distributed normal distributions.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 965835, 13 pages.

Dates
First available in Project Euclid: 28 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364475868

Digital Object Identifier
doi:10.1155/2012/965835

Mathematical Reviews number (MathSciNet)
MR2984034

Zentralblatt MATH identifier
1253.90234

Citation

Wang, Lei; Wang, Xing; Huang, Nan-jing. Tractable Approximation to Robust Nonlinear Production Frontier Problem. Abstr. Appl. Anal. 2012 (2012), Article ID 965835, 13 pages. doi:10.1155/2012/965835. https://projecteuclid.org/euclid.aaa/1364475868


Export citation

References

  • A. Ben-Tal and A. Nemirovski, “Robust convex optimization,” Mathematics of Operations Research, vol. 23, no. 4, pp. 769–805, 1998.
  • A. Ben-Tal and A. Nemirovski, “Robust solutions of uncertain linear programs,” Operations Research Letters, vol. 25, no. 1, pp. 1–13, 1999.
  • A. Ben-Tal and A. Nemirovski, “Robust solutions of linear programming problems contaminated with uncertain data,” Mathematical Programming, vol. 88, no. 3, pp. 411–424, 2000.
  • A. Ben-Tal and A. Nemirovski, “Robust optimization–-methodology and applications,” Mathematical Programming, vol. 92, no. 3, pp. 453–480, 2002.
  • A. Ben-Tal, A. Nemirovski, and C. Roos, “Robust solutions of uncertain quadratic and conic quadratic problems,” SIAM Journal on Optimization, vol. 13, no. 2, pp. 535–560, 2002.
  • D. Bertsimas and M. Sim, “The price of robustness,” Operations Research, vol. 52, no. 1, pp. 35–53, 2004.
  • D. Bertsimas and M. Sim, “Tractable approximations to robust conic optimization problems,” Mathematical Programming, vol. 107, no. 1-2, pp. 5–36, 2006.
  • L. El Ghaoui and H. Lebret, “Robust solutions to least-squares problems with uncertain data,” SIAM Journal on Matrix Analysis and Applications, vol. 18, no. 4, pp. 1035–1064, 1997.
  • L. El Ghaoui, F. Oustry, and H. Lebret, “Robust solutions to uncertain semidefinite programs,” SIAM Journal on Optimization, vol. 9, no. 1, pp. 33–52, 1999.
  • L. Wang and N. J. Huang, “Robust solutions to uncertain weighted least čommentComment on ref. [13?]: Please update the information of this reference, if possible.squares problems,” Mathematical Communications. In press.
  • R. M. Solow, Book Review, vol. 36, New York Times, 1987.
  • C. Carrado and L. Slifman, “A decomposition of productivity and costs,” American Economic Review, vol. 89, pp. 328–332, 1999.
  • A. N. Perakis and A. Denisis, “A survey of short sea shipping and its propescts in the USA,” Maritime Policy and Management, vol. 35, no. 6, pp. 591–614, 2008.
  • J. Yan, X. Sun, and J. Liu, “Assessing container operator efficiency with heterogeneous and time-varying production frontiers,” Transportation Research B, vol. 43, no. 1, pp. 172–185, 2009.