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 feasibili ty of all iterates, for inequality constrained optimization. The methods ba sed 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 prob lem. The method we propose here enjoys some advantages over similar methods based on the equality part of the KKT optimality condition. For example, w ithout assuming isolatedness of the accumulation point or boundedness of th e Lagrangian multiplier approximation sequence, we show that every accumula tion point of the iterative sequence generated by this method is a KKT poin t if the linear independence condition holds. And if the second-order suffi cient condition and the strict complementarity condition hold, the methods superlinearly convergent. Some preliminary numerical results indicate that this new QP-free methods quite promising.