A Sequential Quadratic Programming Method for Nonlinear Programming without a Penalty or a Filter

This paper describes a new algorithm for solving nonlinear programming problems with inequality constraints. The proposed approach first solves a sequence of quadratic programming sub problems with a trust region framework and to induce global convergence, it establishes a new step acceptance mechanism that is neither a penalty function or a filter. Nonmonotone technique from the unconstraint optimization is used to accelerate the algorithm. Under some reasonable assumptions, the method can be proved to be globally convergent to a KT point. Preliminary numerical experiments are presented that show the potential efficiency of the new approach.