二阶PVT算法

Second Order PVT Algorithm

文章在PVT算法中利用负曲率方向,替代了牛顿方向,弥补了Hesse阵不是半正定时牛顿方向不存在的缺点。通过二阶步长准则确定步长因子的策略来求解并行步中的子间题,得到了一个修正的PVT算法。该算法构造的点列收敛到的点,满足极小点的二阶必要条件,故称为二阶PVT算法。

In this paper, negative curvature directions substitute for Newton directions in PVT algorithm. It can make up a dis-disadvantage that Newton direc-tions are nonexistent if Hesse matrix is not semidefinite. The second order step criterion can be used to determine the step factor In order to solve the subproblem）n parallelling step. Then a modified PVT algorithm can be obtained. The point sequences which are created by this algorithm can converge to a ponit. This point satisfies the second order necessary conditions of minimum piont. So this algorithm is styled second order PVT algorithm.