References & Further Reading

References

  1. S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004. [Link]

    The definitive reference for convex optimisation. Chapters 2–5 cover sets, functions, problems, and duality. Available free online.

  2. D. P. Bertsekas, Nonlinear Programming, Athena Scientific, 3rd ed., 2016

    Deep treatment of KKT conditions, duality, and iterative methods. More theoretical than Boyd & Vandenberghe.

  3. J. Nocedal and S. J. Wright, Numerical Optimization, Springer, 2nd ed., 2006

    The standard reference for iterative algorithms: gradient descent, quasi-Newton methods, line search, trust region.

  4. D. P. Palomar and M. Chiang, A Tutorial on Decomposition Methods for Network Utility Maximization, IEEE Journal on Selected Areas in Communications, 2006

    Excellent tutorial on applying Lagrangian duality and decomposition to wireless network optimisation.

  5. Z.-Q. Luo, W.-K. Ma, A. M.-C. So, Y. Ye, and S. Zhang, Semidefinite Relaxation of Quadratic Optimization Problems, IEEE Signal Processing Magazine, 2010

    Survey of SDP relaxation techniques for MIMO detection, beamforming, and sensor network localisation.

  6. Q. Shi, M. Razaviyayn, Z.-Q. Luo, and C. He, An Iteratively Weighted MMSE Approach to Distributed Sum-Utility Maximization for a MIMO Interfering Broadcast Channel, IEEE Transactions on Signal Processing, 2011

    The WMMSE algorithm — the most widely used iterative method for MIMO interference management.

  7. A. Nemirovski, Interior Point Polynomial Time Methods in Convex Programming, Lecture Notes, 2004

    Concise treatment of interior-point methods and their polynomial complexity.

Further Reading

For readers who want to go deeper into specific topics from this chapter.

  • Interior-point methods and polynomial-time algorithms

    Ye, *Interior Point Algorithms: Theory and Analysis*, Wiley, 1997

    Goes deeper into the theory behind interior-point solvers (CVXPY, MOSEK, SeDuMi) that we use as black boxes.

  • Submodularity in machine learning and signal processing

    Krause & Golovin, "Submodular Function Maximization," in *Tractability*, Cambridge, 2014

    Connects submodularity to sensor placement, feature selection, and active learning — all relevant to wireless network design.

  • Distributed optimisation via ADMM

    Boyd et al., "Distributed Optimization and Statistical Learning via ADMM," *Foundations and Trends in ML*, 2011

    ADMM is the workhorse for distributed beamforming and resource allocation in heterogeneous networks (Chapter 23).

  • Online convex optimisation

    Hazan, *Introduction to Online Convex Optimization*, 2nd ed., MIT Press, 2022

    Extends batch optimisation to sequential decision-making — relevant to adaptive resource allocation in time-varying channels.

ExercisesCh 4 →