If b is negative, log(sum（inv_pos(x+a)）+b) may not be convex. If b is positive, I think it is convex, so perhaps @Michal_Adamaszek has a reformulation.

Thanks for your guidance. b is positive.
I find a solution.
cvx_begin
variable x(n,1)
variable y(n,1)
maximize(-y)
subject to
b.*e^{-y} + sum(e^{-y-log(x+a)})<=1;
cvx_end