About snake equation (1)

Reference source ：(6 A private letter / 20 Bar message ) What is gradient descent method ？ - You know (zhihu.com) ------------ Ma classmate

snake The final solution of the equation involves the gradient descent method

Gradient descent method Gradient descent method is used to calculate the optimal value of function

                            

Calculate the optimal value in high numbers, such as ： 

To obtain its minimum value, we need to solve the following equations ：

Now we don't need this method to solve the optimal value

principle ：

   Gradient vector

Suppose the starting point is , That is, put the ball on

                

  Its gradient is 1 Dimension vector ：

  This is     Vector on the axis , It points to the direction of the fastest growth of function value , and It points to the fastest direction of reduction ：

                                    

  take It can also be seen as 1 Dimension vector , Through the and Add up , It can be directed to Move a distance to get a new vector

                                

  among It's called step size , Through it, you can control the moving distance , Through it, you can control the moving distance , set up , that

                   

  At this time, the ball （ That's the starting point ） Down to

                         

  iteration

  The gradient of ：

 

  Continue walking in the opposite direction of the gradient ：

 

The ball rolled to a lower position ：

                                 

Repeat the above process until 10 Time , The ball basically reached the lowest point , That is to say