Communication networks are linked to and influenced by human interactions. Socially-aware systems should integrate these complex relationship patterns in the network design. This paper studies the impact of friendship and antagonistic relationships between individuals on optimal network propagation policies. We develop a network propagation model for signed networks, and determine the optimal policies to influence a target node with an opinion while minimizing the total number of persons against it. We also provide extensions to this problem to elaborate on the impact of network parameters, such as minimum-delay propagation, while limiting the number of persons influenced against the idea before reaching the target. We provide numerical evaluations in a synthetic setup as well as the Epinions online social dataset. We demonstrate that propagation schemes with social and influence-centric constraints should take into account the relationship types in network design.