含边界在内的一般极值的必要条件与拉格朗日乘数法

Necessary Condition for General Local Extremum of Functions and Lagrange Multiplier Rule

讨论包括定义域边界点在内的极值,称为一般极值.对可导的一元和多元函数给出了一般极值点的必要条件,这些必要条件与经典极值的必要条件是相容的.还利用一般极值的必要条件导出了条件极值的拉格朗日乘数法.

Necessary conditions for a class of general local extremum of one-variable and multivariate functions are proposed,these general local extrema may occur at boundary points of the domain.Lagrange multiplier rule is deduced by the necessary condition of the general extremum.