Revision as of 11:08, 27 January 2015

QE2013_AC-3_ECE580-5

Solution:

From the constraint, it can be seen that:

$$ x_1 = x_3 = -x_2 $$

Substitute into the objective function:

$$ f(x) = x_2 (x_1 + x_3) = -2 x_2^2 $$

Therefore it has a maximizer but no minimizer (f(x) goes to $-\infty$ as $$ |x_2| $$ increases)

The maximizer is $$ x_1 = x_2 = x_3 = 0 $$ . There f(x) reaches the maximum value of 0.

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 [[Category:optimization]]
-=QE2013_AC-3_ECE580-4=
+=QE2013_AC-3_ECE580-5=
 :[[QE2013_AC-3_ECE580-1|Part 1]],[[QE2013_AC-3_ECE580-2|2]],[[QE2013_AC-3_ECE580-3|3]],[[QE2013_AC-3_ECE580-4|4]],[[QE2013_AC-3_ECE580-5|5]]
 <br> '''Solution: ''' <br>
+From the constraint, it can be seen that:
+<math>x_1 = x_3 = -x_2 </math>
+Substitute into the objective function:
+<math>f(x) = x_2 (x_1 + x_3) = -2 x_2^2 </math>
+Therefore it has a maximizer but no minimizer (f(x) goes to <math>-\infty</math> as <math>|x_2|</math> increases)
+The maximizer is <math>x_1 = x_2 = x_3 = 0</math>.  There f(x) reaches the maximum value of 0.
 [[ QE2013 AC-3 ECE580|Back to QE2013 AC-3 ECE580]]