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We form the lagrangian:<br> | We form the lagrangian:<br> | ||
<math>l(x,\lambda)=x_1x_2+\lambda_1(x_1+x_2+x_3-1)+\lambda_2(x_1+x_2-x_3)</math><br> | <math>l(x,\lambda)=x_1x_2+\lambda_1(x_1+x_2+x_3-1)+\lambda_2(x_1+x_2-x_3)</math><br> | ||
| − | <math>\begin{cases}\ | + | <math>\begin{cases} |
| + | \nabla_xl=\begin{bmatrix} x_2+\lambda_1+\lambda_2 \\ x_1+\lambda_1+\lambda_2 \\ \lambda_1+\lambda_2\end{bmatrix}=\begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix} \\ | ||
x_1+x_2+x_3-1=0 \\ | x_1+x_2+x_3-1=0 \\ | ||
x_1+x_2-x_3=0 | x_1+x_2-x_3=0 | ||
\end{cases} | \end{cases} | ||
| − | </math> | + | </math><br> |
| + | No valid solution for lagrangian condition <br> | ||
| + | Such that the problem can not be optimized<br> | ||
| + | ---- | ||
| + | ===Similar Problem=== | ||
| + | [https://engineering.purdue.edu/ECE/Academics/Graduates/Archived_QE_August_2015/AC-3?dl=1 2015 QE AC3 Prob1]<br> | ||
| + | [https://engineering.purdue.edu/ECE/Academics/Graduates/Archived_QE_August_2015/AC-3?dl=1 2015 QE AC3 Prob3]<br> | ||
| + | [https://engineering.purdue.edu/ECE/Academics/Graduates/Archived_QE_August_2014/AC-3.pdf?dl=1 2014 QE AC3 Prob2]<br> | ||
---- | ---- | ||
[[QE2016_AC-3_ECE580|Back to QE AC question 3, August 2016]] | [[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]] | ||
Latest revision as of 11:45, 25 February 2019
Automatic Control (AC)
Question 3: Optimization
August 2016 Problem 4
Solution
We form the lagrangian:
$ l(x,\lambda)=x_1x_2+\lambda_1(x_1+x_2+x_3-1)+\lambda_2(x_1+x_2-x_3) $
$ \begin{cases} \nabla_xl=\begin{bmatrix} x_2+\lambda_1+\lambda_2 \\ x_1+\lambda_1+\lambda_2 \\ \lambda_1+\lambda_2\end{bmatrix}=\begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix} \\ x_1+x_2+x_3-1=0 \\ x_1+x_2-x_3=0 \end{cases} $
No valid solution for lagrangian condition
Such that the problem can not be optimized
Similar Problem
2015 QE AC3 Prob1
2015 QE AC3 Prob3
2014 QE AC3 Prob2
