I want to solve a convex function (proven), but it always prompts me that it does not comply with the DCP rules

[uniquelmy]

I still can’t solve this problem, Can anyone give me some advice?

[Mark_L_Stone]

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).

[uniquelmy]

Thank you for your reply. You help me a lot！

[Erling (Erling D.Andersen)]

I would do

t_j = H_j - \sum_i \beta_j x_{ij} \geq 0

and then

\sum_j H_j \mbox{inv_pos}(t_j)

in the objective. It is likely to be more efficient.