非线性规划中最小变化拟Newton方法的局部收敛性

THE LOCAL CONVERGENCE OF LEAST CHANGE QUASINEWTON METHODS FOR NONLINEAR PROGRAMMING PROBLEMS

<正> 考虑非线性规划问题:[1]和[4]曾讨论对某点x处的投影Hesse阵z(x)~T?_(xx)~2L(x,λ)z(x)进行变尺度校正算法的收敛性.假设f(x),c_i(x),i=1,…,t为二次连续可微函数,x~*为(1.1)的解,且在x~*处满足二阶充分性条件。

In this paper, the local convergence of the quasi-Newton methods of Colemanand Conn (1984) for the nonlinear programming problems is analysed, and the leastchange updates of Dennis and Schnabel(1979), and Grzegorski (1985) are used toapproximate the projected Hessian matrix of the Lagrangian function. Furthermore,it is demonstrated that the sequence {x_i} will converge 2-step Q-superlinearly to asolution x~*. The discussion includes fixed-scale and rescaled least change quasi-Newton updates, and their inverse quasi-Newton updates.