QP-free Method Without A Penalty Function

Optimization problem has various important applications in economics, management, engineering, transportation etc. The so-called optimization is to find the best option or solution among the many possible options or methods. The nonlinear constrained optimization problem is one of the most important research subjects. One of the most effective methods is sequential quadractive programming approach. But its computational scale is large, and even its subproblem has no solution. Then the QP-free method is propused. Moreover the sequential quadratic programming may not convergent if the initial point is far away from the solution. To solve this problem, the penalty function is proposed. But it is difficult to choose a suitable penalty parameter. In order to avoid the difficulties of penalty functions, Fletcher and Leyffer propose a filter method is in 2002. Because of good global convergence and numerical results, filter methods resrive more attentions. Notice that the trial point need to compares with all the points in the filter. Some improved methods are proposed in this paper.Based on the QP-free method, filter method and filter-free-type method. We propuse the QP-free self-adaption filter method and QP-free NCP function method without a penalty function and a filter for nolinearprogramming. The major work of this paper is as following:(i) Based on the filter method, QP-free self-adaption filter method is proposed. It is more flexible and easizer to implement with the relax monotonicity compared with other exist filter method.(ii) Based on the QP-free filte rmethod, we propose a QP-free method without a penalty function nor a filter for nolinear programming. The scale of computation is greatly reduced. And the global convergent properties are given under suitable conditions.