I try to solve a maximization problem using CVX. In its simplest form, I want to maximize

f(x,y)=y*h_b\left(\frac{x}{y}\right),

where h_b(\cdot) is the binary entropy function. In the context of CVX, it can be written as

$$f(x,y)=y*\left(entr\left(\frac{x}{y}\right)+entr\left(1-\frac{x}{y}\right)\right).$$

The conditions that I want to impose is as 1 \geq x \geq 0, 1 \geq y \geq 0, y \geq x.

While the function f(x,y) is a concave function, it’s not accepted by CVX. Do you have any suggestions regarding that? Thanks.