LC^1类优化问题的Broyden算法的收敛性分析

SUPERLINEAR CONVERGENCE OF BROYDEN METHODS FOR LC 1 OPTIMIZATION PROBLEMS

本文讨论了利用Ｂｒｏｙｄｅｎ算法求解ＬＣ１类优化问题．所谓ＬＣ１类优化问题是指目标函数一阶连续可微，且它的导函数Ｌｉｐｓｃｈｉｔｚ连续．若假设目标函数是强凸的，讨论了该算法的全局收敛性；若假设目标函数是半光滑的。

In this paper, we show the Broyden methods for solving nonlinear programming problems whose objective functions have locally Lipschitzian derivatives, and discuss the global superlinear convergence under the condition of semismoothness.