In mathematical optimization problems, Lagrange multiplier method (named after mathematician Joseph-Louis Lagrange) is a method to find the extreme value of multivariate function whose variables are limited by one or more conditions. This method transforms an optimization problem with n variables and k constraints into an extreme value problem of a system of equations with n+k variables, and its variables are not subject to any constraints. This method introduces a new scalar unknown, that is, Lagrange multiplier: the coefficient of each vector in the linear combination of gradient of constraint equation. [1] The proof of this method involves partial differential, total differential or chain method, so as to find the unknown value that can make the differential of implicit function zero.
Chinese name
lagrange multiplier method
Foreign name
lagrange multiplier method
express
L=f(x，y，z)+λφ(x，y，z)
presenter
joseph louis lagrange
Show time
179 1 year