The spread of invasive species to new areas threatens the stability of ecosystems and causes major economic losses in agriculture and forestry. We propose a novel approach to minimizing the spread of an invasive species given a limited intervention budget. We first model invasive species propagation using Hawkes processes, and then derive closed-form expressions for characterizing the effect of an intervention action on the invasion process. We use this to obtain an optimal intervention plan based on an integer programming formulation, and compare the optimal plan against several ecologically-motivated heuristic strategies used in practice. We present an empirical study of two variants of the invasive control problem: minimizing the final rate of invasions, and minimizing the number of invasions at the end of a given time horizon. Our results show that the optimized intervention achieves nearly the same level of control that would be attained by completely eradicating the species, with a 20% cost saving. Additionally, we design a heuristic intervention strategy based on a combination of the density and life stage of the invasive individuals, and find that it comes surprisingly close to the optimized strategy, suggesting that this could serve as a good rule of thumb in invasive species management.