# Parallel and Distributed Methods for Nonconvex Optimization--Part II: Applications

arXiv: https://arxiv.org/abs/1601.04059 · HTML: https://mlsanity.com/paper/1601.04059/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2016.

## Built on by (most cited first, 10 of 10)

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- [Coded Computation across Shared Heterogeneous Workers with Communication Delay](https://mlsanity.com/paper/2109.11246/) (2021)
- [Personalized incentives as feedback design in generalized Nash equilibrium problems](https://mlsanity.com/paper/2203.12948/) (2022)
- [Learning Multi-Frequency Partial Correlation Graphs](https://mlsanity.com/paper/2311.15756/) (2023)
- [Online Client Scheduling and Resource Allocation for Efficient Federated Edge Learning](https://mlsanity.com/paper/2410.10833/) (2024)
- [Analog RF Computing: A New Paradigm for Energy-Efficient Edge AI Over MU-MIMO Systems](https://mlsanity.com/paper/2605.14331/) (2026)
- [Operational Regimes in Non-Convex Optimization: A Multiplier-Based Taxonomy](https://mlsanity.com/paper/2609.00471/) (2026)

## Abstract (arXiv)

In Part I of this paper, we proposed and analyzed a novel algorithmic framework for the minimization of a nonconvex (smooth) objective function, subject to nonconvex constraints, based on inner convex approximations. This Part II is devoted to the application of the framework to some resource allocation problems in communication networks. In particular, we consider two non-trivial case-study applications, namely: (generalizations of) i) the rate profile maximization in MIMO interference broadcast networks; and the ii) the max-min fair multicast multigroup beamforming problem in a multi-cell environment. We develop a new class of algorithms enjoying the following distinctive features: i) they are distributed across the base stations (with limited signaling) and lead to subproblems whose solutions are computable in closed form; and ii) differently from current relaxation-based schemes (e.g., semidefinite relaxation), they are proved to always converge to d-stationary solutions of the aforementioned class of nonconvex problems. Numerical results show that the proposed (distributed) schemes achieve larger worst-case rates (resp. signal-to-noise interference ratios) than state-of-the-art centralized ones while having comparable computational complexity.