摘要
讨论多元函数的极值或最值问题,常用的方法是利用多元函数极值的充分条件或拉格朗日乘数法,但运算过程往往比较复杂.对其中的某些问题,如果巧妙地利用目标函数或约束条件的几何性质,则解题思路简捷,而且运算简便,是一种求解多元函数的极值或最值问题的有效方法.但在应用这种方法时,往往是凭经验或直觉,而忽略这种方法的理论根据.通过3个定理给出了这种方法的合理性的说明,并且给出了这种方法的应用.
To discuss extreme value or maximum and minimum values of multivariate function, it is a common method to make use of the sufficient condition of extreme value of multivariate function or to make use of lagrange multiplier method, but the operation process is usually more complicated. To some problems of it, it is thought most convenient to solve the problem if skillfully make use of objective function or constraint conditional properties, and it is a kind of valid method which solves this kind of problem. While applying this kind of method, it is by experience or the intuition usually and usually neglect the theories basis of it. Given the elucidation of the rationality of this kind of method through three theorem, and an application of this kind of method was also given.
出处
《高师理科学刊》
2008年第2期36-37,共2页
Journal of Science of Teachers＇College and University
关键词
多元函数
极值
几何解法
function of many variables
extreme value
geometric solution
