The objective function is \max x-\frac{1}{4}\exp^(-2x)+\frac{1}{9}\exp^(-3x), which is a concave function on x indeed. But CVX can not understand it. So, I wonder if there is any way to express it to make it understandable for CVX. Well, there are more complicated convex constraints so I can not directly solve it.
There are some typos above. \max x-\frac{1}{4}e^{-2x}+\frac{1}{9}e^{-3x}.
If its monotonic, then maximize /minimize x instead. If its not, divide it into two monotonic pieces, then minimize/maximize x. This means you’ll have two subproblems.
Many thanks for your reply. That helps a lot. But I may not convey my problem precisely. The problem exists in the constraints. The form is like $t \leq x-\frac{1}{4}e^{-2x}+\frac{1}{9}e^{-3x}$，which is convex indeed but not understandable for CVX. Is there any way to express the constraint in cvx?