I need to find the step size

Miguel Hanson

Miguel Hanson

Answered question

2022-04-09

I need to find the step size αk when considering function Q(x)=12xTAx+bTx
I know that the gradient(g) is Axb and I should minimize the function
Φ(α)=Q(xkαg(xk))
I am stuck after putting the values into Φk(α) and even that I am not sure of doing correctly. Can you help me with the Φk(α) function and if possible give some directions on what to do next?

Answer & Explanation

glanzerjbdo

glanzerjbdo

Beginner2022-04-10Added 13 answers

Step 1
The gradient is Ax+b
If you differentiate Φk(α) with respect to α using chain rule and set it to 0, we should get
g(xk)T[A(xkαg(xk))+b]=0
g(xk)T[g(xk)αAg(xk)]=0
I will leave the task of isolating α to you.

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