Automatic Control (AC)

Question 3: Optimization

August 2016 Problem 2

### Solution

a) From the Optimization textbook, Zak Stanislaw. Lemma 8.3

For fixed step gradient descent algorithms $ \alpha $ should in the range $ (0,\dfrac{2}{\lambda max(Q)}) $

b) $ Q=\begin{bmatrix} 12 & 0 \\ 0 & 4 \end{bmatrix} $

such that $ \lambda max(Q)=12 \Rightarrow \alpha \in (0, \dfrac{1}{6}) $