An Algorithm for Solving Quadratic Optimization Problems with Nonlinear Equality Constraints

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.