An infeasible QP-free method without a penalty function for nonlinear inequality constrained optimization

In this paper, we present a new QP-free method without using a penalty function for inequality constrained optimization. It is an infeasible method. At each iteration, three linear equations with the same coefficient matrix are solved. The nearly active set technique is used in the algorithm, which eliminates some inactive constraints and reduces the dimension of coefficient matrix, and thereby reduces the amount of computational work. Moreover, the algorithm reduces the value of objective function or the measure of constraints violation according to the relationship between optimality and feasibility. Under common conditions, we prove that the proposed method has global and superlinear local convergence. Lastly, preliminary numerical results are reported.