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Duality and solutions for quadratic programming over single non-homogeneous quadratic constraint

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Listed:
  • Joe-Mei Feng
  • Gang-Xuan Lin
  • Reuy-Lin Sheu
  • Yong Xia

Abstract

This paper extends and completes the discussion by Xing et al. (Canonical dual solutions to the quadratic programming over a quadratic constraint, submitted) about the quadratic programming over one quadratic constraint (QP1QC). In particular, we relax the assumption to cover more general cases when the two matrices from the objective and the constraint functions can be simultaneously diagonalizable via congruence. Under such an assumption, the nonconvex (QP1QC) problem can be solved through a dual approach with no duality gap. This is unusual for general nonconvex programming but we can explain by showing that (QP1QC) is indeed equivalent to a linearly constrained convex problem, which happens to be dual of the dual of itself. Another type of hidden convexity can be also found in the boundarification technique developed in Xing et al. (Canonical dual solutions to the quadratic programming over a quadratic constraint, submitted). Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • Joe-Mei Feng & Gang-Xuan Lin & Reuy-Lin Sheu & Yong Xia, 2012. "Duality and solutions for quadratic programming over single non-homogeneous quadratic constraint," Journal of Global Optimization, Springer, vol. 54(2), pages 275-293, October.
    • Handle: RePEc:spr:jglopt:v:54:y:2012:i:2:p:275-293
    DOI: 10.1007/s10898-010-9625-6
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    References listed on IDEAS

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    1. Harish Palanthandalam-Madapusi & Tobin Van Pelt & Dennis Bernstein, 2009. "Matrix pencils and existence conditions for quadratic programming with a sign-indefinite quadratic equality constraint," Computational Optimization and Applications, Springer, vol. 45(4), pages 533-549, December.
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    Cited by:

    1. Matamala, Yolanda & Feijoo, Felipe, 2021. "A two-stage stochastic Stackelberg model for microgrid operation with chance constraints for renewable energy generation uncertainty," Applied Energy, Elsevier, vol. 303(C).
    2. Duy-Van Nguyen, 2022. "Strong Duality for General Quadratic Programs with Quadratic Equality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 297-313, October.
    3. A. Taati & M. Salahi, 2019. "A conjugate gradient-based algorithm for large-scale quadratic programming problem with one quadratic constraint," Computational Optimization and Applications, Springer, vol. 74(1), pages 195-223, September.

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