A New Globally and Superlinearly Convergent QP- Free Method for Inequality Constrained Optimization

Abstract:

Based on a non-smooth equation of KKT optimality condition, this paper presents a new QPfree method for inequality constrained optimization by using the Fischer-Burmeister NCP function, which ensures the feasibility of all iterates and makes it unnecessary to search along an arc. To avoid Maratos effect, a high-order modified correction is introduced. Compared with the traditional SQP method, this new method only needs to solve no more than three systems of linear equation per iteration with global convergence and local superlinear convergence under some reachable conditions. Without assuming isolateness of the accumulation point or boundedness of the Lagrangian multiplier approximation sequence, every accumulation point of the iterative sequence generated by this method is a KKT point.