Explain Lagrange’s method of undetermined multipliers.
Answers
In mathematical optimization, the method of Lagrange multipliers (or method of Lagrange's undetermined multipliers, named after Joseph-Louis Lagrange) is a strategy for finding the local maxima and minima of a function subject to equality constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables). The great advantage of this method is that it allows the optimization to be solved without explicit parameterization in terms of the constraints. As a result, the method of Lagrange multipliers is widely used to solve challenging constrained optimization problems.
The method can be summarized as follows :-
1) isolate any possible singular point of the solution set of the constraining equations,
2) find all the stationary points of the Lagrange function,
3) establish which of those stationary points and singular points are global maxima (or minima, in case of minimization problems) of the objective function.
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