Strongly convex problem has UNBOUNDED status using CVX

Question

I am trying to minimize a function of the following type:

f(x)=LogSumExp(Ax)+b'*x+||x||^2

Using CVX in MATLAB, CVX outputs "Status: Unbounded Optimal value (cvx_optval): -Inf"

This is not reasonable given the fact it is a strongly convex function. Any idea why I get this and how to solve it?

For instance, to get this type of output, I run the simple example:

A= rand(10,10)

b=-10^4*ones(10,1)

cvx_begin
    variable z(10)
    minimize(log_sum_exp(A*z)+z'*z+b'*z)
    subject to 
        z>=0
cvx_end