基于目标函数梯度向量的相邻方向共轭法

从共轭梯度法的基本思想出发,在前一寻优方向起点和终点的负梯度向量平移所决定的平面内确定共轭方向,并提出二维和三维优化问题的共轭方向计算公式。根据向量的几何关系和矢量加减运算的几何意义,推导由任一寻优方向起点和终点的梯度所确定的共轭方向。此方法可用于多维优化问题的求解。提出新算法的寻优步骤,并与众多经典共轭方向计算公式相比。该算法不仅具有理论严密性,而且寻优有效,具有二次终止性。

Conjugate Method of Adjacent Directions Based on Gradient Vector of Objective Function

Starting from the basic concept of conjugate gradient method,the conjugate direction was con-firmed in the plane,which was determined by the translation of the negative gradient vector at the starting point and the end point of the previous optimization direction,and the conjugate directions calculation for-mula of two-dimensional and three-dimensional optimization problems were presented.According to the ge-ometric relationship of vectors and the geometric meaning of vector addition and subtraction,the conjugate direction determined by the gradient of the starting point and the end point of any optimization direction was deduced.This method could be used to solve the multidimensional optimization problem.The optimiza-tion procedure of the new algorithm was proposed.Compared with many classical conjugate direction calcu-lation formulas,the algorithm was not only theoretical rigorous,but also efficient and had quadratic termi-nability.