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A branch and bound algorithm for quantified quadratic programming

Author

Listed:
  • F. Domes

    (University of Vienna)

  • A. Goldsztejn

    (CNRS, IRCCYN (UMR 6597))

Abstract

The aim of this paper is to find the global solutions of uncertain optimization problems having a quadratic objective function and quadratic inequality constraints. The bounded epistemic uncertainties in the constraint coefficients are represented using either universal or existential quantified parameters and interval parameter domains. This approach allows to model non-controlled uncertainties by using universally quantified parameters and controlled uncertainties by using existentially quantified ones. While existentially quantified parameters could be equivalently considered as additional variables, keeping them as parameters allows maintaining the quadratic problem structure, which is essential for the proposed algorithm. The branch and bound algorithm presented in the paper handles both universally and existentially quantified parameters in a homogeneous way, without branching on their domains, and uses some dedicated numerical constraint programming techniques for finding a robust, global solution. Several examples clarify the theoretical parts and the tests demonstrate the usefulness of the proposed method.

Suggested Citation

  • F. Domes & A. Goldsztejn, 2017. "A branch and bound algorithm for quantified quadratic programming," Journal of Global Optimization, Springer, vol. 68(1), pages 1-22, May.
    • Handle: RePEc:spr:jglopt:v:68:y:2017:i:1:d:10.1007_s10898-016-0462-0
    DOI: 10.1007/s10898-016-0462-0
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    References listed on IDEAS

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    1. Mian Li & Steven Gabriel & Yohan Shim & Shapour Azarm, 2011. "Interval Uncertainty-Based Robust Optimization for Convex and Non-Convex Quadratic Programs with Applications in Network Infrastructure Planning," Networks and Spatial Economics, Springer, vol. 11(1), pages 159-191, March.
    2. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    3. V. Jeyakumar & G. Li, 2013. "Robust solutions of quadratic optimization over single quadratic constraint under interval uncertainty," Journal of Global Optimization, Springer, vol. 55(2), pages 209-226, February.
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    Cited by:

    1. Marendet, Antoine & Goldsztejn, Alexandre & Chabert, Gilles & Jermann, Christophe, 2020. "A standard branch-and-bound approach for nonlinear semi-infinite problems," European Journal of Operational Research, Elsevier, vol. 282(2), pages 438-452.

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