How to express I2=log(sum(inv_pos()))

Log( {convex} ) is almost the same as your problem, except that you would need log(sigma^2) instead of 0 as the first element in the argument of log_sum_exp And you need to divide log_sum_exp by log(2) Then use t in place of log2(...), so -t in place of -log2(...) . The model will only be correct if you use -t in a way in which concave would be allowed.