A Smoothing QP-free Infeasible Method without a Penalty Function and a Filter

Abstract

In this paper, we propose a smoothing QP-free infeasible method without a penalty function and a filter for inequality constrained nonlinear optimization problems. This iterative method is based on smoothing equations which are the reformulation of the KKT first-order optimality conditions, by using the multipliers and the smoothing NCP function. Comparing with other QP-free method, in each iteration, the new algorithm only needs to solve two systems of smoothing linear equations with the same nonsingular coefficient matrix. It does not request the strict feasibility of the iterations including the initial point. We demand the reduction of either the objective function or part of the reformulation of KKT conditions per iteration without a penalty function and a filter. This method is implementable and globally convergent. Under mild conditions, we prove that the method has super linear convergence rate. Some numerical results show that the new method is effective.