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拉格蘭吉乘數

第三十一單元. 拉格蘭吉乘數. Constrained Optimization Problem. A One-variable problem. Lagrange. Joseph-Louis Lagrange (1736-1813) Mathematician who developed many fundamental techniques in the calculus of variations, including the method that bears his name. Geometric Interpretation. Lagrange Method.

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拉格蘭吉乘數

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  1. 第三十一單元 拉格蘭吉乘數

  2. Constrained Optimization Problem A One-variable problem

  3. Lagrange Joseph-Louis Lagrange (1736-1813) Mathematician who developed many fundamental techniques in the calculus of variations, including the method that bears his name.

  4. Geometric Interpretation

  5. Lagrange Method

  6. Lagrange Theorem

  7. Procedure for the Method of Lagrange

  8. Example

  9. Example

  10. Example(continued)

  11. Example(continue)

  12. Example

  13. Example(continued)

  14. Animate plot 3d

  15. Example

  16. Example (Optimization inside a Region)

  17. Solution:

  18. Solution(continued)

  19. 單元結語 • 有限制條件的極值問題除了特定的狀況可使用歌西不等式、算 幾的方法外，拉格蘭吉乘子法都可以算。 • 拉格蘭吉乘子法不限於於只有一個限制條件，兩個、三個限制條件都可以解，在此為避免計算過於冗長，所舉得例題只做一個限制條件的問題。

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