Approximation algorithms for indefinite complex quadratic maximization problems

In this paper, we consider the following indefinite complex quadratic maximization problem: maximize z H Qz , subject to z k ∈ ℂ and z k m = 1, k = 1,..., n , where Q is a Hermitian matrix with tr Q = 0, z ∈ ℂ n is the decision vector, and m ⩾ 3. An Ω(1/log n ) approximation algorithm is presented f...

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Bibliographic Details
Published inScience China. Mathematics Vol. 53; no. 10; pp. 2697 - 2708
Main Authors Huang, Yongwei, Zhang, Shuzhong
Format Journal Article
LanguageEnglish
Published Heidelberg SP Science China Press 01.10.2010
Subjects
Applications of Mathematics
Mathematics
Mathematics and Statistics
approximation ratio
90C20
indefinite Hermitian matrix
randomized algorithms
90C22
semidefinite programming relaxation
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Summary:In this paper, we consider the following indefinite complex quadratic maximization problem: maximize z H Qz , subject to z k ∈ ℂ and z k m = 1, k = 1,..., n , where Q is a Hermitian matrix with tr Q = 0, z ∈ ℂ n is the decision vector, and m ⩾ 3. An Ω(1/log n ) approximation algorithm is presented for such problem. Furthermore, we consider the above problem where the objective matrix Q is in bilinear form, in which case a approximation algorithm can be constructed. In the context of quadratic optimization, various extensions and connections of the model are discussed.
ISSN:1674-7283
1862-2763
DOI:10.1007/s11425-010-3087-7