  The classical method to solve a quadratic optimization problem with nonlinear
equality constraints is to solve the Karush-Kuhn-Tucker (KKT) optimality
conditions using Newton's method. This approach however is usually
computationally demanding, especially for large-scale problems. This paper
presents a new computationally efficient algorithm for solving quadratic
optimization problems with nonlinear equality constraints. It is proven that
the proposed algorithm converges locally to a solution of the KKT optimality
conditions. Two relevant application problems, fitting of ellipses and state
reference generation for electrical machines, are presented to demonstrate the
effectiveness of the proposed algorithm.
