Constrained Optimization

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This Demonstration shows the minimization or maximization of a function (blue) subject to a constraint (red). The green point shows the optimal solution.

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The graphic on the left shows the level curves of and together with the gradients. On the right, a 3D graphic of the function is shown together with the constraint of projected onto the surface of .

For either the minimum or maximum, the gradients of the function and the constraint are parallel: , with the Lagrange multiplier . By moving the point around the plot region, you can see that this is a necessary condition for constrained optimization.

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Contributed by: Edda Eich-Soellner (University of Applied Sciences, München, Germany) (March 2011)
Open content licensed under CC BY-NC-SA


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Permanent Citation

Edda Eich-Soellner (University of Applied Sciences, München, Germany) "Constrained Optimization"
http://demonstrations.wolfram.com/ConstrainedOptimization/
Wolfram Demonstrations Project
Published: March 7 2011

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