Global convergence of an improved QP-free method based on linear equations

In this paper, we propose an improved QP-Free method for nonlinear inequality constrained optimization based on linear equations. This new algorithm only needs to solve two systems of linear equations. It has the following advantages: (1) the amount of computation is greatly reduced; (2) the good nature of the descent directions is fully used; (3) the obtained search direction is feasible. Under some suitable assumptions, the global convergence of the new algorithm is proved.