Efficient Optimization Algorithms for Generalized Multi-Group Multicast Beamforming

In this article, we propose a new approach to solve the max-min fair user association problem in multi-user MIMO (Multiple Input, Multiple Output) systems. The goal is to assign users to base stations (BSs) in a way that maximizes the overall system performance while minimizing the difference in performance between the best and worst-performing user groups.
To tackle this problem, we first reformulate it into a convex optimization framework, which involves introducing auxiliary variables to linearize the objective function and adding constraints to ensure feasibility. This approach allows us to solve the problem using existing convex optimization techniques.
However, this reformulation comes with an increased optimization dimension, which can lead to computational complexity issues. To address this challenge, we propose a new algorithm called Convex-Concave Proximal Gradient Descent (CM-PAGD), which combines the benefits of proximal gradient descent and convex-concave optimization techniques.
The proposed approach is based on the idea of approximating the non-smooth objective function using a smooth surrogate function, which allows us to solve the problem using a more efficient optimization method. We also propose a new technique called Linearized Subgradient Method (LSM), which leverages the subgradient property of the non-smooth objective function to achieve faster convergence.
We demonstrate the effectiveness of our proposed approach through simulations and compare it with existing methods in terms of computational complexity and performance. Our results show that the proposed CM-PAGD method achieves better performance while reducing the computational complexity compared to existing approaches.
In summary, this article presents a new approach to solve the max-min fair user association problem in multi-user MIMO systems by reformulating it into a convex optimization framework and proposing efficient optimization techniques to mitigate computational complexity issues. Our proposed method achieves better performance while reducing computational complexity, making it a valuable contribution to the field of wireless communication networks.