Considering the following optimization program:

$$ maximize \ \ \ \log \left( \|x\|_\infty \right) $$

$$ subject \ to \ \ \ \ Ax\leq b $$

can we rewrite this program as a convex equivalence?

Considering the following optimization program:

$$ maximize \ \ \ \log \left( \|x\|_\infty \right) $$

$$ subject \ to \ \ Ax\leq b, \ x \geq 0 $$

can we rewrite this program as a convex equivalence?