A rank preserving flow algorithm for quadratic optimization problems subject to quadratic equality constraints

• Published in: 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing Vol. 1; pp. 67 - 70 vol.1
• Main Authors: Moore, J.B., Danchi Jiang
• Format: Conference Proceeding
• Language: English
• Published: Washington DC IEEE 1997; IEEE Computer Society Press
• Subjects: Antennas; Applied sciences; Costs; Exact sciences and technology; Information, signal and communications theory; Linear matrix inequalities; Mathematical methods; Matrix converters; Polynomials; Radiocommunications; Symmetric matrices; Telecommunications; Telecommunications and information theory; Vectors
• ISBN: 0818679190; 9780818679193
• ISSN: 1520-6149
• DOI: 10.1109/ICASSP.1997.599549

This paper concerns quadratic programming problems subject to quadratic equality constraints such as arise in broadband antenna array signal processing and elsewhere. At first, such a problem is converted into a semidefinite programming problem with a rank constraint. Then, a rank preserving flow is used to accommodate the rank constraint. The associated gradient formulas are carefully developed. The convergence of the resulting algorithm is also guaranteed. Our approach is demonstrated by a numerical experiment.