An interior point method for nonlinear programming with infeasibility detection capabilities

This paper describes interior point methods for nonlinear programming endowed with infeasibility detection capabilities. The methods are composed of two phases, a main phase whose goal is to seek optimality, and a feasibility phase that aims exclusively at improving feasibility. A common characteristic of the algorithms is the use of a step-decomposition interior-point method in which the step is the sum of a normal component and a tangential component. The normal component of the step provides detailed information that allows the algorithm to determine whether it should be in main phase or feasibility phase. We give particular attention to the reliability of the switching mechanism between the two phases. The two algorithms proposed in this paper have been implemented in the knitro package as extensions of the knitro/cg and knitro/direct methods. Numerical results illustrate the performance of our methods on both feasible and infeasible problems.