That is log of the complementary cumulative Normal distribution function. The sum of logs complicates things. But we can see that this is non-convex even if there is no sum (i.e., sum has one term).
Exponentiate (6) and then take log again, resulting in log_normcdf(u) <= log(1-exp(alpha)) . This is going in the wrong direction to be convex, because log_normcdf is concave.