Determining step size using golden ratio
I would like to calculate the minimum of the function using the steepest descent method. I am, however, stuck at determining the step size. I want to calculate the step size using golden ratio, however, as I have only use the method in 1 dimension, I don't know how to use it here. Here is what I did so far:
Step 1: Choose starting points. These were given already as
Step 2: Calculate the gradient . I did this and got . Substituting for the starting points , we get
Step 3: Calculate .
I am stuck at step 3. I don't know how I can get . If there is a possibility to use the golden ratio to determine alpha here, I would welcome. Any help in explaining it is highly appreciated. Thanks in advance!
Re: Determining step size using golden ratio
If you know what to do in 1-dimension, it's easy to apply the algorithm in 2-dimensions. Just considers the 1-d function :
And apply the method on .