A superlinearly convergent numerical algorithm for nonlinear programming

In this paper, a new algorithm is proposed to solve the nonlinear constrained optimization problems. Unlike sequential quadratic programming (SQP) type methods, this algorithm does not involve solutions of quadratic programs. It is merely necessary to solve systems of linear equations with small scale to obtain a direction. The scheme is based on an idea of εε-effective active set strategies. The theoretical analysis shows that global and superlinear convergence can be induced under some suitable conditions.