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

Joe Mei Feng, Gang Xuan Lin, Reuy Lin Sheu, Yong Xia

Research output: Contribution to journalArticle

19 Citations (Scopus)

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).

Original languageEnglish
Pages (from-to)275-293
Number of pages19
JournalJournal of Global Optimization
Volume54
Issue number2
DOIs
Publication statusPublished - 2012 Oct 1

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All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Management Science and Operations Research
  • Control and Optimization
  • Applied Mathematics

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