A QP-free algorithm without a penalty function or a filter for nonlinear general-constrained optimization

Abstract

In this paper, we present a QP-free algorithm without a penalty function or a filter for nonlinear general-constrained optimization. At each iteration, three systems of linear equations with the same coefficient matrix are solved to yield search direction; the nonmonotone line search ensures that the objective function or constraint violation function is sufficiently reduced. There is no feasibility restoration phase in our algorithm, which is necessary for filter methods. The algorithm possesses global convergence as well as superlinear convergence under some mild conditions including a weaker assumption of positive definiteness. Finally, some preliminary numerical results are reported.