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===Radio resource management===
The purpose of [[radio resource management]] is to satisfy the data rates that are requested by the users of a cellular network.<ref name="GOLBO16">{{Cite book |url=http://cdn.intechopen.com/pdfs-wm/53332.pdf |doi=10.5772/66.399| isbn=9781466557529|title=Beamforming in Wireless Networks|year=2016|last1=Golbon-Haghighi|first1=M.H. |journal=InTech Open| pages=163-199}}</ref><ref name=fnt2013>E. Björnson and E. Jorswieck, [http://kth.diva-portal.org/smash/get/diva2:608533/FULLTEXT01 Optimal Resource Allocation in Coordinated Multi-Cell Systems], Foundations and Trends in Communications and Information Theory, vol. 9, no. 2-3, pp. 113-381, 2013.</ref> The main resources are time intervals, frequency blocks, and transmit powers. Each user has its own objective function that, for example, can represent some combination of the data rate, latency, and energy efficiency. These objectives are conflicting since the frequency resources are very scarce, thus there is a need for tight spatial [[frequency reuse]] which causes immense inter-user interference if not properly controlled. [[Multi-user MIMO]] techniques are nowadays used to reduce the interference by adaptive [[precoding]]. The network operator would like to both bring great coverage and high data rates, thus the operator would like to find a Pareto optimal solution that balance the total network data throughput and the user fairness in an appropriate subjective manner.
Radio resource management is often solved by scalarization; that is, selection of a network utility function that tries to balance throughput and user fairness. The choice of utility function has a large impact on the computational complexity of the resulting single-objective optimization problem.<ref name=fnt2013 /> For example, the common utility of weighted sum rate gives an [[NP-hard]] problem with a complexity that scales exponentially with the number of users, while the weighted max-min fairness utility results in a quasi-convex optimization problem with only a polynomial scaling with the number of users.<ref name=luo2008>Z.-Q. Luo and S. Zhang, [http://www.ece.umn.edu/~luozq/assets/pdf/publications_files/Zhang08.pdf Dynamic spectrum management: Complexity and duality], IEEE Journal of Selected Topics in Signal Processing, vol. 2, no. 1, pp. 57–73, 2008.</ref>
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