An Lp norm relaxation approach to positive influence maximization in social network under the deterministic linear threshold model

Abstract

In this paper, an Influence Maximization problem in Social Network under the Deterministic Linear Threshold model is considered. The objective is to minimize the number of eventually negatively opinionated nodes in the network in a dynamic setting. The main ingredient of the new approach is the application of the sparse optimization technique. In the presence of inequality constraints and nonlinear relationships, the standard convex relaxation method of the L 1 relaxation does not perform well in this context. Therefore we propose to apply the L p relaxation where 0 < p < 1. The resulting optimization model is therefore non-convex. By means of an interior point method, the model can be solved efficiently and stably, typically yielding robust and sparse solutions in our numerical experiments with the simulated data. © 2013 Springer International Publishing.