Decomposition methods for Network Utility Maximization (NUM)

“Efficiently Solve” a NUM problem

1. Theoretical properties

Such as global optimality and duality gap.

Convex optimization: minimizing a convex function over a convex constraint set.
For a convex optimization, a local optimum is also a global optimum and the duality is zero under mild conditions.

2. Computational properties

To solve convex optimization, there are provably polynomial-time and practically fast and scalable (but centralized) algorithms. (e.g., interior-point methods)

3. Decomposability structures

Decomposability structures may lead to distributed (and often iterative) algorithms that converge to the global optimum.

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[~] D. P. Palomar and Mung Chiang, “A tutorial on decomposition methods for network utility maximization,” in IEEE Journal on Selected Areas in Communications, vol. 24, no. 8, pp. 1439-1451, Aug. 2006.