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

  • Authors:

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

  • Affiliations:

  • Department of Mathematics, National Cheng Kung University, Tainan, Taiwan;Department of Mathematics, National Cheng Kung University, Tainan, Taiwan;Department of Mathematics, National Cheng Kung University, Tainan, Taiwan;LMIB of the Ministry of Education, School of Mathematics and System Sciences, Beihang University, Beijing, People's Republic of China

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2012

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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).