改进的拉氏乘子法和多变量广义变分原理

拉氏乘子法是构造广义变分原理的重要途径 ,在识别拉氏乘子时 ,拉氏乘子是独立变分的 ,而识别后 ,它却是其他变量的函数 ,这是产生临界变分的原因 .本文对拉氏乘子法作了改进 ,提出了一种新的理论——凑合反推法 ,应用该方法可以方便地构造多变量的广义变分原理 ,并且不会出现临界变分现象

Modified Lagrange Multiplier Method and Its Application to the Establishment of Generalized Variational Principles

The general approach to the establishment of generalized variational principle is the well\|known Lagrange multiplier method. In this method, the multipliers are considered as independent variables during the procedure of identification of the multipliers, however, after identification, they all become functions of the other variables, i.e. the multipliers are not independent variables, contradicting the a priori assumption. The paper illustrates that the so\|called variational crisis (some Lagrange multiplier become zero) is the intrinsic shortcomings of the method, which can be completely overcome by the semi\|inverse method proposed by the present author.