Approximation algorithms for indefinite complex quadratic maximization problems - Huang, Yongwei; Zhang, Shuzhong (Science China. Mathematics, 2010)
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.