A simple feasible SQP method for inequality constrained optimization with global and superlinear convergence

In this paper, a simple feasible SQP method for nonlinear inequality constrained optimization is presented. At each iteration, we need to solve one QP subproblem only. After solving a system of linear equations, a new feasible descent direction is designed. The Maratos effect is avoided by using a high-order corrected direction. Under some suitable conditions the global and superlinear convergence can be induced. In the end, numerical experiments show that the method in this paper is effective.