The growth of the Internet has fueled the development of new technologies that enable IP backbone networks to be engineered efficiently. One such prominent technology, Multiprotocol label switching (MPLS) enables IP networks with Quality of Service to be traffic engineered well. In this paper, we mathematically formulate the traffic engineering problems in MPLS based IP networks including constraint based routing, connection admission control, rerouting and capacity planning problems. Unfortunately, obtaining the optimal solution of the traffic engineering problems has undesirable computational complexity since they can be shown to be NP-complete. It is intended that this work will articulate the details and provide insights into the inherent structure of the problems as well as motivate the development of efficient solution techniques.