We consider the problem of influence maximization in fixed networks, for both stochastic and adversarial contagion models. In the stochastic setting, nodes are infected in waves according to linear threshold or independent cascade models. We establish upper and lower bounds for the influence of a subset of nodes in the network, where the influence is defined as the expected number of infected nodes at the conclusion of the epidemic. We quantify the gap between our upper and lower bounds in…

We present an extension of the Frank-Wolfe method that is designed to induce near-optimal solutions on low-dimensional faces of the feasible region. We present computational guarantees for the method that trade off efficiency in computing near-optimal solutions with upper bounds on the dimension of minimal faces of iterates. We apply our method to the low-rank matrix completion problem, where low-dimensional faces correspond to low-rank solutions. We present computational results for large-scale low-rank matrix completion problems that demonstrate significant speed-ups in…