无罚函数和滤子的QP-free非可行域方法

提出了求解光滑不等式约束最优化问题的无罚函数和无滤子QP-free非可行域方法. 通过乘子和非线性互补函数, 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-拟牛顿迭代得到满足KKT最优性条件的解, 在迭代中采用了无罚函数和无滤子线搜索方法, 并证明该算法是可实现，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.

QP-free infeasible method without a penalty function and a filter

In this paper, we propose a QP-free infeasible method without a penalty function and a filter for constrained nonlinear optimization problems. This iterative method is based on the solution of nonsmooth equations which are obtained by the multipliers and the piecewise linear relationship NCP function for the KKT first-order optimality conditions. Locally, each iteration of this method can be viewed as a perturbation of the mixed Newton-quasi Newton iteration on both primal and dual variables for the solution of KKT optimality conditions. We do not use a penalty function and a filter on line searches.This method is implementable and globally convergent. Without the second order correction we prove that the method has superlinear convergence rate under some mild conditions.