滤子QP-free算法

Filter QP-free Method

提出了求解光滑不等式约束最优化问题的滤子QP-free非可行域方法.通过乘子函数和F-B非线性互补函数,构造一个等价于原约束问题一阶KKT条件的非光滑方程组.在此基础上,通过牛顿、拟牛顿迭代得到KKT最优条件的解,在迭代的线搜索中,采用了滤子方法.证明了该方法是可以实现的并具有全局收敛性.另外,在较弱条件下可以证明该方法具有超线性收敛性.

This paper presents a filter QP-free infeasible method for minimizing a smooth function subjected to smooth inequality constraints. This iterative method is based on the solution of nonsmooth equations obtained by the multiplier and some nonlinear complementarity problem（ NCP） functions for the KKT first-order optimality conditions. 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 is also adopted in the linear searches. This method is implementable and globally convergent. The method proves to be of super linear convergence rate under some mild conditions.