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a) From the Optimization textbook, Zak Stanislaw. Lemma 8.3<br> | a) From the Optimization textbook, Zak Stanislaw. Lemma 8.3<br> | ||
For fixed step gradient descent algorithms <math>\alpha</math> should in the range <math>(0,\dfrac{2}{\lambda max(Q)})</math><br> | For fixed step gradient descent algorithms <math>\alpha</math> should in the range <math>(0,\dfrac{2}{\lambda max(Q)})</math><br> | ||
| − | b) <math> | + | b) <math>Q=\begin{bmatrix} 12 & 0 \\ 0 & 4 \end{bmatrix}</math><br> |
such that <math>\lambda max(Q)=12 \Rightarrow \alpha \in (0, \dfrac{1}{6})</math><br> | such that <math>\lambda max(Q)=12 \Rightarrow \alpha \in (0, \dfrac{1}{6})</math><br> | ||
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[[ECE_PhD_Qualifying_Exams|Back to ECE Qualifying Exams (QE) page]] | [[ECE_PhD_Qualifying_Exams|Back to ECE Qualifying Exams (QE) page]] | ||
Latest revision as of 15:19, 19 February 2019
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}) $
