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

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.