非线性规划的QP-free方法

QP-free Method for Nonlinear Programming Problems

该文提出一种QP-free可行域方法用来解满足光滑不等式约束的最优化问题.此方法把QP-free方法和3-1线性互补函数相结合一个等价于原约束问题的一阶KKT条件的方程组,并在此基础上给出解这个方程组的迭代算法.这个方法的每一步迭代都可以看作是对求KKT条件解的牛顿或拟牛顿迭代的扰动,且在该方法中每一步的迭代均具有可行性.该方法是可实行的且具有全局性,且不需要严格互补条件、聚点的孤立性和积极约束函数梯度的线性独立等假设.在与文献[2]中相同的适当条件下,此方法还具有超线性收敛性.数值检验结果表示,该文提出的QP-free可行域方法是切实有效的方法.

In this paper,A QP-free feasible method is proposed to obtain the local convergence under some weaker conditions for the minimization of a smooth function subject to smooth inequalities.Based on the solutions of linear systems of equation reformulation of the KKT optimality conditions,this method uses the 3-1 NCP function.The method is iterative,which means each iteration can be viewed as a perturbation of a Newton or Quasi Newton on both the primal and dual variables for the solution of the equalities in the KKT first order conditions of optimality,and the feasibility of all iterations is ensured in this method.In particular,this method is implementable and globally convergent without assuming the strict complementarity condition,the isolation of the accumulation point and the linear independence of the gradients of active constrained functions.The method has also superlinear convergence rate under some mild conditions which are the same as those in[2].Some preliminary numerical results indicate that this new QP-free feasible method is quite promising.