How to represent this expression in CVX

1

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If there anyone know how to represent this expression in CVX？Only B_k is variable . Thanks advance！

2

-rel_entr(Bk,Bk+p*hk/N0)/log(2) >= Rmin

In general, x*log(1+y/x) can be formulated as -rel_entr(x,x+y) .presuming x is affine and y is concave (note that a numerical constant is concave).

3

Thanks for your help. I am very sorry that there is another problem :is that can achieve in CVX? Only B_k is variable too. And constraint of B_k is :0<=B_k <=B_max(a constant)
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4

You can apply inv_pos, because it accepts a concave argument.

minimize(Lk*inv_pos(-rel_entr(Bk,Bk+p*hk/N0)/log(2)))
0 <= Bk <= B_max

help inv_pos

inv_pos Reciprocal of a positive quantity.
inv_pos(X) returns 1./X if X is positive, and +Inf otherwise.
X must be real.

 For matrices and N-D arrays, the function is applied to each element.

  Disciplined convex programming information:
      inv_pos is convex and nonincreasing; therefore, when used in CVX
      specifications, its argument must be concave (or affine).

You may benefit from a careful reading of the CVX Users’ Guide http://cvxr.com/cvx/doc/ , as well as the Mosek Modeling Cookbook https://docs.mosek.com/modeling-cookbook/index.html