How to express the function in CVX?

1

I want to express this function in CVX:

fomula
fomula2305×698 870 KB

According to the perspective function, the concavity of part ② equals to the concavity of -log2(1+p), which is convex. So the function is convex.

My code is as follow
variables mu_t,beta,p are nonnegative; B,D,No,h are constant;
miut - Bbeitalog2(1+phinv_pos(NoBbeita)) <= 0;

When I running it , I got this error
Disciplined convex programming error:
Cannot perform the operation: {real affine} .* {convex}

2

Use rel_entr(). Check http://web.cvxr.com/cvx/doc/funcref.html#new-functions.

3

Thanks for the tip. I have tried rel_entr() before, but I can only represent xlog(1+x/y), not ylog(1+x/y), can you provide a more detailed representation？Thank you！

4

ylog(1+x/y)=-ylog(y/(x+y))=-rel_entr(y,x+y). It can be written this way because (y,x+y) is a linear mapping of (x,y)，then the rule of composition of convex function applies.

5

Oh I see! Thank you so much!