Minimizing an indefinite quadratic function subject to a single indefinite quadratic constraint. (2nd January 2018)

• Record Type: Journal Article
• Authors: Fallahi, S.; Salahi, M.; Terlaky, T.
• Is Part Of: Optimization. Volume 67:Number 1(2018)
• Page Start: 55
• Page End: 65
• Publication Date: 2018-01-02
• Subjects: Indefinite quadratic optimization -- global optimization -- diagonalization -- semidefinite optimization relaxation; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1388378
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: In this paper, we consider the problem of minimizing an indefinite quadratic function subject to a single indefinite quadratic constraint. A key difficulty with this problem is its nonconvexity. Using Lagrange duality, we show that under a mild assumption, this problem can be solved by solving a linearly constrained convex univariate minimization problem. Finally, the superior efficiency of the new approach compared to the known semidefinite relaxation and a known approach from the literature is demonstrated by solving several randomly generated test problems.