解约束优化问题的QP-free非可行域方法

提出了一种新的QP-free非可行域方法，用来解不等式约束的最优化问题．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．在此基础上给出解这方程组的迭代算法．与QP-free可行域方法相比较，在不要求迭代点严格可行性的情况下，此方法是可执行的．在不要求严格互补松弛成立、聚点是孤立的，以及积极约束函数梯度是线性独立等条件下，证明该方法具有全局收敛性．另外在较弱的条件下，证明该方法具有超线性收敛性．

Convergence of QP-Free Infeasible Methods for Nonlinear Inequality Constrained Optimization Problems

In this paper,a new QP-free infeasible methods is proposed for minimizing a smooth function subject to smooth inequallity constraints.This iterative method is based on the solution of nonsmooth ~equations which are obtained by the multipliers and some nonlinear complementarity problem(NCP) functions for the KKT first-order optimality conditions.Comparing with other QP-free methods,our method does not request the strict feasibility.In particular,this method is implementable and globally convergent without assuming the strict complementarity condition,isolatedness of the accumulation point and linear independence of the gradients of active constrained functions at the solution.We also prove that the method has superlinear convergence rate under some mild conditions.