约束最优化问题中一个全局误差界及其应用

本文利用信赖域方法中的几个特征量(由预测下降量给出的价值函数与信赖域半径等),在目标函数的梯度向量是强单调的条件下,为约束最优化问题的可行解与最优解之间的距离提供了一个全局误差界。我们利用误差界得出了可行解点列收敛于最优解的充分条件和可行解点列收敛到KT点的必要条件。最后,还给出了可行解点列至KT点集的距离趋于零的必要条件。

A Global Error Bound of Constrained Optimization Problem and its Applications

In this paper,by using some characteristic quantities such as value function,trust region radius,etc. in trust region method,we present a global error bound for the distance between a feasible solution and the optimal solution under the condition that the gradient vector of the objective function is strongly monotone. Using this error bound,we give a sucient condition which guarantees a feasible solution sequence converges to a optimal solution and a necessary condition under which a feasible solution sequence converges to a KT point. Finally,we get a necessary condition under which the distance between a feasible sequence and the KT point set converges to zero.