[machine learning 03] Lagrange multiplier method

 

Catalog

1 The shortest distance from the origin

 2 contour

3 Lagrange multiplier method  

​ edit 4 Lagrange multiplier method   Definition

5 Multiple constraints

4 Extreme value under inequality constraint

5 KTT Conditions

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How to understand Lagrange multiplier method ？ In optimization problems in Mathematics , Lagrange multiplier method （ With mathematician Joseph · Lagrange named ） It is a method to find the extreme value of multivariate function when its variable is constrained by one or more conditions .https://mp.weixin.qq.com/s/wpJ3db4fvqe_il6N3AQs4A

How to understand Lagrange multiplier method and KKT Conditions ？ This article will continue to introduce the details of Lagrange multiplier method , And promote it properly （ It's called KKT Conditions ）.https://mp.weixin.qq.com/s/SnHGG7ZEZ9SJapPmWhhHpQ 

1 The shortest distance from the origin

  Now we want to find the shortest distance between the point on it and the origin ：

 

 

 2 contour

 

3 Lagrange multiplier method  

 

4 Lagrange multiplier method   Definition

 

 

5 Multiple constraints

 

 

4 Extreme value under inequality constraint

Look directly at the second link

In the link 4.3 New conditions   about Why under inequality constraints , The first formula above is equal to 0.

The direction of the objective function and the gradient descent function is opposite .

5 KTT Conditions