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

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  • Joe-Mei Feng
  • Gang-Xuan Lin
  • Reuy-Lin Sheu

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  • Yong Xia
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    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

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    File URL: http://hdl.handle.net/10.1007/s10898-010-9625-6
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    Bibliographic Info

    Article provided by Springer in its journal Journal of Global Optimization.

    Volume (Year): 54 (2012)
    Issue (Month): 2 (October)
    Pages: 275-293

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    Handle: RePEc:spr:jglopt:v:54:y:2012:i:2:p:275-293

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    Web page: http://www.springer.com/business/operations+research/journal/10898

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    Related research

    Keywords: Non-convex quadratic programming; Simultaneously diagonalizable via congruence; Slater’s condition; Duality; Hidden convexity;

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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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