一种带滤子的QP-free非可行域方法

A QP-free Infeasible Methods with Filter

摘要:

提出了一种带滤子的QP-free非可行域方法,用来解不等式约束的最优化问题.此方法通过乘子函数和3-1线性互补函数构造一个等价于原约束问题的一阶KKT条件的非光滑方程组,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,在线性搜索时用到滤子方法.这个方法是可实行的且具有全局性,并且在适当的条件下还可以得到此方法的超线性收敛性.用此算法进行了数值检验,结果表明此方法是可行有效的.

Abstract:

A filter QP-free infeasible method is proposed for minimizing a smooth function subject to smooth inequality constraints.This method is introduced by solving nonsmooth equations which are equivalent to the KKT first-order optimality conditions that are constructed by the multiplier and some NCP functions.Locally,each iteration of this method can be viewed as a perturbation of a Newton or quasi-Newton iteration on both the primal and dual variables for the solution of the KKT optimality conditions.The filter method is also used in linear search.This method is implementable and globally convergent.The method proves to have superlinear convergence rate under some mild conditions.The computational results show that this algorithm is efficient and reliable.