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Robust solutions of quadratic optimization over single quadratic constraint under interval uncertainty

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  • V. Jeyakumar
  • G. Li

Abstract

In this paper we examine non-convex quadratic optimization problems over a quadratic constraint under unknown but bounded interval perturbation of problem data in the constraint and develop criteria for characterizing robust (i.e. uncertainty-immunized) global solutions of classes of non-convex quadratic problems. Firstly, we derive robust solvability results for quadratic inequality systems under parameter uncertainty. Consequently, we obtain characterizations of robust solutions for uncertain homogeneous quadratic problems, including uncertain concave quadratic minimization problems and weighted least squares. Using homogenization, we also derive characterizations of robust solutions for non-homogeneous quadratic problems. Copyright Springer Science+Business Media, LLC. 2013

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  • 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.
    • Handle: RePEc:spr:jglopt:v:55:y:2013:i:2:p:209-226
    DOI: 10.1007/s10898-012-9857-8
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    References listed on IDEAS

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    1. Vaithilingam Jeyakumar & Zhiyou Wu, 2007. "Conditions For Global Optimality Of Quadratic Minimization Problems With Lmi Constraints," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 24(02), pages 149-160.
    2. B. T. Polyak, 1998. "Convexity of Quadratic Transformations and Its Use in Control and Optimization," Journal of Optimization Theory and Applications, Springer, vol. 99(3), pages 553-583, December.
    3. Dimitris Bertsimas & David B. Brown, 2009. "Constructing Uncertainty Sets for Robust Linear Optimization," Operations Research, INFORMS, vol. 57(6), pages 1483-1495, December.
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    Cited by:

    1. 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.

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