(Created page with "Category:ECE Category:QE Category:problem solving <center> <font size= 4> ECE Ph.D. Qualifying Exam </font size> <font size= 4> Auto...") |
|||
| Line 23: | Line 23: | ||
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> | ||
---- | ---- | ||
| − | [[QE2016_AC-3_ECE580|Back to QE AC question | + | [[QE2016_AC-3_ECE580|Back to QE AC question 3, August 2016]] |
[[ECE_PhD_Qualifying_Exams|Back to ECE Qualifying Exams (QE) page]] | [[ECE_PhD_Qualifying_Exams|Back to ECE Qualifying Exams (QE) page]] | ||
Revision as of 12:24, 18 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) $ f(x)-\dfrac{1}{2}x^TQx-b^Tx=\dfrac{1}{2}x^T\begin{bmatrix} 12 & 0 \\ 0 & 4 \end{bmatrix}-5 $
such that $ \lambda max(Q)=12 \Rightarrow \alpha \in (0, \dfrac{1}{6}) $
