A New QP-Free, Globally Convergent, Locally Superlinearly Convergent Algorithm For Inequality Constrained Optimization

In this paper, we propose a new QP-free method, which ensures the feasibility of all iterates, for inequality constrained optimization. The method is based on a nonsmooth equation reformulation of the KKT optimality condition, by using the Fischer--Burmeister nonlinear complementarity problem function. The study is strongly motivated by recent successful applications of this function to the complementarity problem and the variational inequality problem. The method we propose here enjoys some advantages over similar methods based on the equality part of the KKT optimality condition. For example, without assuming isolatedness of the accumulation point or boundedness of the Lagrangian multiplier approximation sequence, we show that every accumulation point of the iterative sequence generated by this method is a KKT point if the linear independence condition holds. And if the second-order sufficient condition and the strict complementarity condition hold, the method is superlinearly convergent. Some preliminary numerical results indicate that this new QP-free method is quite promising.