Constrained Optimization: Lagrange Multipliers

Constrained Optimization: Lagrange Multipliers

When trying to optimize a particular quantity in the real world, there are usually natural constraints such as a fixed amount of money for an investment, or fixed dimensions on which to build in a plot of land. In such circumstances, the methods for finding local minima and maxima we have so far considered will not work, so we need an alternate way to solve such problems.

This worksheet introduces the idea of Lagrange Multipliers to solve the problem of finding global minima and maxima of a function subject to a fixed constraint. It also considers the generalization to finding global minima and maxima subject to an inequality.