About: Lagrange multiplier   Sponge Permalink

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Using a Lagrange multiplier is a method of finding an extreme value of a function with a constraint; for example, finding the extreme values of which is constrained by . This will occur when the contour lines of the function are parallel, the gradients will therefore be parallel as well (since the gradient vector is always orthogonal to the contour lines). As such, the Lagrange multiplier is a scalar such that Which results in four unknowns and four equations. This can be represented more concisely with the Lagrangian function

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  • Lagrange multiplier
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  • Using a Lagrange multiplier is a method of finding an extreme value of a function with a constraint; for example, finding the extreme values of which is constrained by . This will occur when the contour lines of the function are parallel, the gradients will therefore be parallel as well (since the gradient vector is always orthogonal to the contour lines). As such, the Lagrange multiplier is a scalar such that Which results in four unknowns and four equations. This can be represented more concisely with the Lagrangian function
  • I describe the contents of video to help readers' understanding. We want to minimize subject to . By Lagrange multiplier, we can write the Lagrange multiplier equation as . Use the property of Lagrange multiplier that the partial derivatives of the above Lagrange multiplier equation should be equal to zero From the first and the second equations, we will have and . Putting these results to the third equation, we find , which result that and . Thus, the minimum of becomes .
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abstract
  • Using a Lagrange multiplier is a method of finding an extreme value of a function with a constraint; for example, finding the extreme values of which is constrained by . This will occur when the contour lines of the function are parallel, the gradients will therefore be parallel as well (since the gradient vector is always orthogonal to the contour lines). As such, the Lagrange multiplier is a scalar such that Which results in four unknowns and four equations. This can be represented more concisely with the Lagrangian function
  • I describe the contents of video to help readers' understanding. We want to minimize subject to . By Lagrange multiplier, we can write the Lagrange multiplier equation as . Use the property of Lagrange multiplier that the partial derivatives of the above Lagrange multiplier equation should be equal to zero From the first and the second equations, we will have and . Putting these results to the third equation, we find , which result that and . Thus, the minimum of becomes .
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