Duality and solutions for quadratic programming over single non-homogeneous quadratic constraint
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
Volume (Year): 54 (2012)
Issue (Month): 2 (October)
|Contact details of provider:|| Web page: http://www.springer.com/business/operations+research/journal/10898|
|Order Information:||Web: http://link.springer.de/orders.htm|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
When requesting a correction, please mention this item's handle: RePEc:spr:jglopt:v:54:y:2012:i:2:p:275-293. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla)or (Christopher F Baum)
If references are entirely missing, you can add them using this form.