# Reliable Projection Based Unsupervised Learning for Semi-Definite QCQP with Application of Beamforming Optimization

arXiv: https://arxiv.org/abs/2407.03668 · HTML: https://mlsanity.com/paper/2407.03668/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 14 references that are in the map.
- First posted on arXiv 4 Jul 2024.

## Builds on (most cited first, 6 of 6)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [On the Convergence Rates of Policy Gradient Methods](https://mlsanity.com/paper/2201.07443/) (2022)
- [Graph Neural Networks for Scalable Radio Resource Management: Architecture Design and Theoretical Analysis](https://mlsanity.com/paper/2007.07632/) (2020)
- [Knowledge-Assisted Deep Reinforcement Learning in 5G Scheduler Design: From Theoretical Framework to Implementation](https://mlsanity.com/paper/2009.08346/) (2020)
- [PCNet: A Structure Similarity Enhancement Method for Multispectral and Multimodal Image Registration](https://mlsanity.com/paper/2106.05124/) (2021)
- [Scalable Resource Management for Dynamic MEC: An Unsupervised Link-Output Graph Neural Network Approach](https://mlsanity.com/paper/2306.08938/) (2023)

## Built on by (most cited first, 2 of 2)

- [RadioDiff: An Effective Generative Diffusion Model for Sampling-Free Dynamic Radio Map Construction](https://mlsanity.com/paper/2408.08593/) (2024)
- [GNN-Empowered Effective Partial Observation MARL Method for AoI Management in Multi-UAV Network](https://mlsanity.com/paper/2409.00036/) (2024)

## Abstract (arXiv)

In this paper, we investigate a special class of quadratic-constrained quadratic programming (QCQP) with semi-definite constraints. Traditionally, since such a problem is non-convex and N-hard, the neural network (NN) is regarded as a promising method to obtain a high-performing solution. However, due to the inherent prediction error, it is challenging to ensure all solution output by the NN is feasible. Although some existing methods propose some naive methods, they only focus on reducing the constraint violation probability, where not all solutions are feasibly guaranteed. To deal with the above challenge, in this paper a computing efficient and reliable projection is proposed, where all solution output by the NN are ensured to be feasible. Moreover, unsupervised learning is used, so the NN can be trained effectively and efficiently without labels. Theoretically, the solution of the NN after projection is proven to be feasible, and we also prove the projection method can enhance the convergence performance and speed of the NN. To evaluate our proposed method, the quality of service (QoS)-contained beamforming scenario is studied, where the simulation results show the proposed method can achieve high-performance which is competitive with the lower bound.