Approximation methods for complex polynomial optimization

Bo Jiang (), Zhening Li () and Shuzhong Zhang ()

Computational Optimization and Applications, 2014, vol. 59, issue 1, 219-248

Abstract: Complex polynomial optimization problems arise from real-life applications including radar code design, MIMO beamforming, and quantum mechanics. In this paper, we study complex polynomial optimization models where the objective function takes one of the following three forms: (1) multilinear; (2) homogeneous polynomial; (3) symmetric conjugate form. On the constraint side, the decision variables belong to one of the following three sets: (1) the $$m$$ m -th roots of complex unity; (2) the complex unity; (3) the Euclidean sphere. We first discuss the multilinear objective function. Polynomial-time approximation algorithms are proposed for such problems with assured worst-case performance ratios, which depend only on the dimensions of the model. Then we introduce complex homogenous polynomial functions and establish key linkages between complex multilinear forms and the complex polynomial functions. Approximation algorithms for the above-mentioned complex polynomial optimization models with worst-case performance ratios are presented. Numerical results are reported to illustrate the effectiveness of the proposed approximation algorithms. Copyright Springer Science+Business Media New York 2014

Keywords: Polynomial optimization; Complex programming; Complex tensor; Approximation algorithm; Tensor relaxation; 90C59; 90C10; 15A69; 90C26 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-014-9640-5

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