  Ultra-dense network (UDN) is a promising technology to further evolve
wireless networks and meet the diverse performance requirements of 5G networks.
With abundant access points, each with communication, computation and storage
resources, UDN brings unprecedented benefits, including significant improvement
in network spectral efficiency and energy efficiency, greatly reduced latency
to enable novel mobile applications, and the capability of providing massive
access for Internet of Things (IoT) devices. However, such great promises come
with formidable research challenges. To design and operate such complex
networks with various types of resources, efficient and innovative
methodologies will be needed. This motivates the recent introduction of highly
structured and generalizable models for network optimization. In this article,
we present some recently proposed large-scale sparse and low-rank frameworks
for optimizing UDNs, supported by various motivating applications. A special
attention is paid on algorithmic approaches to deal with nonconvex objective
functions and constraints, as well as computational scalability.
