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

MIDCP
Oct 21, 2023
U
#1

Screenshot 2023-10-21 at 16.16.19

Screenshot 2023-10-21 at 16.16.56
Screenshot 2023-10-21 at 16.16.561876×320 29.7 KB

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

M
#2

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).
1 reply
U
#3
Replying to #2

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

1 reply
E
#4
Replying to #3

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.