采用修正搜索方向的约束变尺度算法

A Class of Constrained Variable Metric Algorithms with Modified Search Direction

以WHP算法为代表的约束变尺度算法是解有约束非线性规划问题的常用算法之一,但是,这类算法还有较多理论问题没有解决。本文提出一类新的约束变尺度算法,而且在不假定‖B_k‖有界的情况下,证明该算法的整体收敛性和在一定条件下,算法超线性收敛。

The Constrained variable algorithms, represented by WHP, are very useful and efficient methods for the constrained nonlinear programming. But some problems for these algorithms have not been solved. In this paper we present a new class of constrained variable metrix algorithms which modify the search direction after each quadric subprogramming. We prove the algorithms are convergent without assuming the variable metric matrices and their inverse bounded, and superlinear convergent with certain conditions.