A line search SQP method without a penalty or a filter

Abstract

This paper describes a new algorithm for nonlinear programming problems with inequality constraints. The proposed approach first solves a sequence of quadratic programming subproblems via the line search technique and to induce the global convergence, it establishes a new step acceptance mechanism that is neither a penalty function nor a filter. A nonmonotone line search technique from the unconstraint optimization is applied to accelerate the algorithm. Under some reasonable assumptions, the method can be proved to be globally convergent to a KT point. Preliminary numerical results are presented that show the potential efficiency of the new approach.