This document provides a detailed description of the tutorial lecture on Challenges in Network Optimization provided at the 2016 IEEE 17th International Conference on High Performance Switching and Routing (HPSR). This lecture is motivated by the recent evolutions of communication networks which have induced new challenges in mixed-integer network optimization ranging from problem formulation to computational methods. Indeed, paradigms such as information-oriented networks, resource abstraction (at the heart of virtualization and other cloudification), and programmability of network functions lead to combine well-established optimization problems with network optimization problems (network design, resource placement/allocation and other multi-commodity flow problems). Beyond dimensioning, provisioning/configuring and scheduling/ planning, the combination of conventional network optimization problems with the facility-location or the hub-location problem for instance, provides guidelines for the design of unified processes that address these evolutions. In this tutorial, we exploit mixed-integer programming as a tool for driving early design decisions (thus, not only for the traditional application of network optimization) together with associated requirements such as congestion awareness but also reliability by extending the combined problems to their reliable variant. We compare how the selection of the appropriate routing strategies may also be determined by means of this approach. Finally, in order to cope with demand uncertainty, we extend these formulations to their set-induced robust counterpart. Indeed, robust optimization enables to accommodate spatio-temporal variations in demands and associated traffic for instance without compromising on the solution quality. We conclude this lecture by outlining some of the main research challenges in network optimization at both modeling and computational level.