I am optimizing a function f

f(x) = \sum_i {log(a_i x + b)} - c x

where x is a vector (the optimization variable), a’s and c are row vectors. b is a scalar constant.

cvx shows the warning that using the log function will require more time as it uses the successive approximation method. Is there any other way to describe the objective function in a way that avoids this?

I am running so many instances, and with such delay, the overall runtime of the program will be very huge.