Comparison of Methods to Detect
Extrema Subject to a Constraint
Return to the main document on extrema subject to a constraint.
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The method of parametrizing the constraint set requires a higher level of ingenuity to get started, because it can be quite difficult to find a parametrization of the given constraint set. The advantage of working with this method is that the second derivative test is now available to us, and it can help us distinguish a local extremum from a saddle point. |
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The method of Lagrange multipliers is usually easy to get started with. However, we have a more complicated system of equations to deal with afterwards. In many cases, this method is adequate to determine the absolute extrema of a function subject to a given constraint. On the other hand, it offers no help whatsoever if we need to distinguish a local extremum from a saddle point.
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Return to the main document on extrema subject to a constraint. |