I'm currently working on this Optimization problem:
$\min \max (|x-2|,|y+1|)$
Subject to
$x,y\geq0$
We have been asked to show the optimal solutions graphically using the fact:
$\max (|x-2|,|y+1|) = ||\boldsymbol m-\boldsymbol c||_\infty$
How do I draw level curves from $z = ||\boldsymbol m-\boldsymbol c||_\infty$ for different values of z?
Also, let's say $z=\max (|x-2|,|y+1|)$ if I was to generate the objective function:
$\min z$
How would I extract the matrix $c^T$ that comes from the standard form:
$\min c^T \boldsymbol x$
Best Answer
Follows a plot for $\max\left(|x-2|,|y+1|\right)$
as well as the correspondent level curves
EDIT
Attached the plotting script. (in MATHEMATICA)