A new penalty-free-type method for nonlinear inequality constrained optimization

In this paper, we present a new penalty-free method for nonlinear inequality constrained optimization, which is a QP-free method. At each iteration, three linear equations with the same coefficient matrix are solved. Moreover, the nearly active set technique is used to improve the computational effect. The algorithm reduces the value of objective function or the measure of constraints violation according to the relationship between optimality and feasibility. Under mild conditions, we prove that the proposed method has global and superlinear local convergence. At last, preliminary numerical results are reported.