Convex Optimization problems arising from Linear systems - Adam Oberman Math

The following minimization of convex piecewise linear functions can be converted into Linear Programming problems, and sometimes also solved directly by ad-hoc methods.

$\min_x \| Ax -b \|_\infty$

$\min_x f(x) = \max ( |x-b_1|, \dots |x-b_k|)$

$\min_x f(x) = \max ( |a_1x-b_1|, \dots |a_k x-b_k|)$

the solution to this one is in the Infinity Laplacian numerics paper