A penalty-function-free line search SQP method for nonlinear programming

We propose a penalty-function-free non-monotone line search method for nonlinear optimization problems with equality and inequality constraints. This method yields global convergence without using a penalty function or a filter. Each step is required to satisfy a decrease condition for the constraint violation, as well as that for the objective function under some reasonable conditions. The proposed mechanism for accepting steps also combines the non-monotone technique on the decrease condition for the constraint violation, which leads to flexibility and an acceptance behavior comparable with filter based methods. Furthermore, it is shown that the proposed method can avoid the Maratos effect if the search directions are improved by second-order corrections (SOC). So locally superlinear convergence is achieved. We also present some numerical results which confirm the robustness and efficiency of our approach.