This post introduces the concept of Lagrangian Optimization. This is a method for finding the local extrema of a multivariable function when the variables are subject to one or more constraint conditions. This method can transform an optimization problem with n variables and k constraint conditions into a problem of solving a system of equations with n + k variables.
这篇帖子介绍了Lagrangian Optimization。这是一种是一种寻找多元函数在其变量受到一个或多个条件的约束时的局部极值的方法。这种方法可以将一个有n个变量与k个约束条件的最优化问题转换为一个解有n + k个变量的方程组的解的问题。
The discussion starts with the case of a single-variable equality constraint, and then gradually generalizes to the cases of multiple-variable equalities and single-variable inequalities.
首先从单变量等式约束条件开始讨论 ,随后逐渐推广到多变量等式，单变量不等式的情况
Finally, the post presents the Lagrangian Optimization equations for the cases of multiple-variable equalities and multiple-variable inequalities.
最后给出多变量等式、多变量不等式对应的Lagrangian Optimization方程