Minimizing an indefinite quadratic function subject to a single indefinite quadratic constraint

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 lin...

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Bibliographic Details
Published inOptimization Vol. 67; no. 1; pp. 55 - 65
Main Authors Fallahi, S., Salahi, M., Terlaky, T.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 02.01.2018
Taylor & Francis LLC
Subjects
diagonalization
global optimization
Indefinite quadratic optimization
Quadratic equations
semidefinite optimization relaxation
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Summary: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.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2017.1388378