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Case Studies for a First-Order Robust Nonlinear Programming Formulation

Author

Listed:
  • E. T. Hale

    (Rice University)

  • Y. Zhang

    (Rice University)

Abstract

In this paper, we conduct three case studies to assess the effectiveness of a recently proposed first-order method for robust nonlinear programming [Zhang, Y.: J. Optim. Theory Appl. 132, 111–124 (2007)]. Three robust nonlinear programming problems were chosen from the literature using the criteria that results calculated using other methods must be available and the problems should be realistic, but fairly simple. Our studies show that the first-order method produced reasonable solutions when the level of uncertainty was small to moderate. In addition, we demonstrate a method for leveraging a theoretical result to eliminate constraint violations. Since the first-order method is relatively inexpensive in comparison to other robust optimization techniques, our studies indicate that, under moderate uncertainty, the first-order approach may be more suitable than other methods for large problems.

Suggested Citation

  • E. T. Hale & Y. Zhang, 2007. "Case Studies for a First-Order Robust Nonlinear Programming Formulation," Journal of Optimization Theory and Applications, Springer, vol. 134(1), pages 27-45, July.
    • Handle: RePEc:spr:joptap:v:134:y:2007:i:1:d:10.1007_s10957-007-9208-y
    DOI: 10.1007/s10957-007-9208-y
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    References listed on IDEAS

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    1. Y. Zhang, 2007. "General Robust-Optimization Formulation for Nonlinear Programming," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 111-124, January.
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    Cited by:

    1. Soleimanian, Azam & Salmani Jajaei, Ghasemali, 2013. "Robust nonlinear optimization with conic representable uncertainty set," European Journal of Operational Research, Elsevier, vol. 228(2), pages 337-344.

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