  Information propagation on networks is a central theme in social, behavioral,
and economic sciences, with important theoretical and practical implications,
such as the influence maximization problem for viral marketing. Here, we
consider a model that unifies the classical independent cascade models and the
linear threshold models, and generalise them by considering continuous
variables and allowing feedback in the dynamics. We then formulate its
influence maximization as a mixed integer nonlinear programming problem and
adopt derivative-free methods. Furthermore, we show that the problem can be
exactly solved in the special case of linear dynamics, where the selection
criterion is closely related to the Katz centrality, and propose a customized
direct search method with local convergence. We then demonstrate the
close-to-optimal performance of the customized direct search numerically on
both synthetic and real networks.
