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求函数极值问題,已有不少的论述。在代数里,讲过y=ax~2+bx+c的图象以后,求二次函数的最大值和最小值得到了较彻底的解决。本文就在此基础上,借助于求解非线性规划问題的思想,用图形来解答一些常见的具有约束条件的极值问题。这类问题的一般形式是:在约束条件下,要求找出变量x_i(i=1,2,…,n)的值,使得给定的函数 L=f(x_1,x_2,…,x_n) (2)取最大值或最小值。这里gi(x_1,x_2,…,x_n) (i=1,2,…,m)和f(x_1,x_2,…,x_n)都是变量x_1,x_2,…,x_n的有理整函数;“V”表示=,≤,≥中的某一个符号。式(2)称为目标函数。
Finding the extremum of functions has been discussed for quite some time. In algebra, after talking about the image of y=ax~2+bx+c, the maximum and minimum values of the quadratic function have been completely solved. Based on this, this paper uses the idea of solving nonlinear programming problems to solve some common extremum problems with constraints. The general form of this type of problem is: Under constraint conditions, it is required to find the value of the variable x_i(i=1,2,...,n) so that the given function L=f(x_1,x_2,...,x_n) ( 2) Take the maximum or minimum value. Here gi(x_1,x_2,...,x_n) (i=1,2,...,m) and f(x_1,x_2,...,x_n) are all rational integer functions of the variables x_1,x_2,...,x_n; “” =, ≤, ≥ one of the symbols. Equation (2) is called the objective function.