a,b are all positive variables，can this constraint be expressed in CVX？

Unlike your previous constraint at Constraint：a*log(1+b/a)>c

if `a`

and `b`

are separate variables, the LHS is neither concave nor convex. Therefore the constraint s non-convex.

my idea is convert this expression to :

a*log(1+c/a)>k,c=a/b ,

then use rel_entr

That is an attempt at convex alchemy. `c = a/b`

is not convex.

If that is the constraint you need, then use a tool such as YALMIP which can accept and attempt to solve non-convex problems