Multiplicadores de Lagrange

Multiplicadores de Lagrange
[size=150][justify]Los multiplicadores de Lagrange te permite encontrar el máximo o o el mínimo de una función multivariable, cuando hay alguna restricción en los valores de entrada que puedes usar.[/justify]La idea central es buscar puntos en donde las curvas de nivel de f y g sean tangentes entre sí. Esto es lo mismo que encontrar puntos en donde los vectores de los gradientes de f y g sean paralelos entre sí.Todo el proceso puede reducirse a hacer el gradiente de una cierta función, llamada el lagrangiano, igual al vector cero.[img 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[/img][/size][br]

Information: Multiplicadores de Lagrange