  This paper proves the consistency property for the regularized maximum
likelihood estimators (MLEs) of multivariate Hawkes processes (MHPs). It also
develops an alternating minimization type algorithm (AA-iPALM) to compute the
MLEs with guaranteed global convergence to the set of stationary points. The
performance of this AA-iPALM algorithm on both synthetic and real-world data
shows that AA-iPALM consistently improves over iPALM and PALM. Moreover,
AA-iPALM is able to identify the causality structure in rental listings on
craigslist and herd behavior in the NASDAQ ITCH dataset.
