Finding the MLE for a univariate exponential Hawkes process

The univariate exponential Hawkes process is a self-exciting point process with an event arrival rate of:

$\lambda(t) = \mu + \sum\limits_{t_i<t}{\alpha e^{-\beta(t-t_i)}}$

where $t_1,..t_n$ are the event arrival times.

The log likelihood function is

$– t_n \mu + \frac{\alpha}{\beta} \sum{( e^{-\beta(t_n-t_i)}-1 )} + \sum\limits_{i<j}{\ln(\mu+\alpha e^{-\beta(t_j-t_i)})}$

which can be calculated recursively:

$– t_n \mu + \frac{\alpha}{\beta} \sum{( e^{-\beta(t_n-t_i)}-1 )} + \sum{\ln(\mu+\alpha R(i))}$

$R(i) = e^{-\beta(t_i-t_{i-1})} (1+R(i-1))$

$R(1) = 0$

What numerical methods can I use to find the MLE? What is the simplest practical method to implement?