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).`

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

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.