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A Hessian-free 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 algorithm which is more computationally efficient, since it does not require either additional optimization variables or computation of the Hessian matrix. It is proven that the proposed algorithm converges locally to a solution of the KKT optimality conditions. An application example is presented to demonstrate the effectiveness of the proposed algorithm.