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§1 迭代方法的基本思想第一讲已讨论了多变量函数(指非线性函数,以下同)极值点存在的必要条件和判别其为极大或极小点的充分条件。当目标函数具有简单且明确的数学表达式时,利用极值理论,把求极值的问题转化为求解目标函数的一阶偏导数为零的方程组,这就是所谓的间接法。但是,多变量函数一般都比较复杂,求解它的一阶偏导数为零的方程组,往往很困难,有时甚至目标函数无明确的数学表达式,间接法就无能为力了,要借助于所谓的直接法。
§1 The basic idea of iterative method The first chapter has discussed the necessary conditions for the existence of the extremum point of a multivariable function (refer to the non-linear function, the same below) and the sufficient conditions for determining whether it is a maximal or minimal point. When the objective function has a simple and definite mathematical expression, the extremum theory is used to convert the problem of finding the extremum into an equation system with zero first-order derivative of the objective function. This is the so-called indirect method. However, multivariable functions are generally complex and it is often difficult to solve their system of equations with first-order partial derivatives of zero. Sometimes, even if the objective function has no explicit mathematical expression, the indirect method can not do anything, by virtue of the so-called direct law.