Disciplined convex programming error: Cannot perform the operation {convex}*{convex}

Hi all,
I am having quite some trouble to implement the function. And the function I have proven is convex. Below is a minimum example of where I am at now. Note that a,b and c is strictly positive.

c16468×313 4.72 KB

The error I get is “Cannot perform the operation {convex}*{convex}”.
Any suggestions on how to improve the code are welcome as well.

Thanks,

Please show us your proof that the objective function is concave. Unless that is the case you cannot use cvx.

Sorry, there is a mistake in my code.The objective function is convex. So the maximize is wrong.Below is the correct one.

c16468×313 4.72 KB

We know that if the function is twice differentiable and the Hessian is positive semidefinite in the entire domain, then the function is convex. Below is the prove:

S__510280531098×999 91.2 KB

So now you changed the problem. Please show that

a*b <= 15
a,b>=0

is a convex constraint i.e. f(a,b) is convex function.

Btw the

geometric mean(t,a,b,b) >= 1

implies

t >= 1/(a*b^2)

So now you can easily handle the objective using the geometric mean function in cvx.

Thanks for your help !! And I’m so sorry. I can’t run the code if there is no constraint before. So i casually add the constraint behind. And didn’t realize the constraint is not convex.
What if this kind of function f(a,b) = a^-1*b^2 (the domain of a,b : a>0,b>0) show up in the constraint. Ex: f(a,b) <= {such a complicated concave function} How to deal with in this situation.

It is for you to figure out which convex problem that make sense for you to solve.

Fully grateful for your reply!!!