How to represent this expression in CVX

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 CVX Users’ Guide — CVX Users' Guide , as well as the Mosek Modeling Cookbook MOSEK Modeling Cookbook — MOSEK Modeling Cookbook 3.3.0