Incorporating a four-dimensional filter line search method into an interior point framework

Abstract

Here we incorporate a four-dimensional filter line search method into an infeasible primal-dual interior point framework for nonlinear programming. Each entry in the filter has four components measuring dual feasibility, complementarity, primal feasibility and optimality. Three measures arise directly from the first order optimality conditions of the problem and the fourth is the objective function, so that convergence to a stationary point that is a minimizer is guaranteed. The primary assessment of the method has been done with a well-known collection of small problems.