# Efficient Global Optimal Resource Allocation in Non-Orthogonal Interference Networks

## TL;DR

This paper introduces a novel, efficient algorithm for solving complex non-convex resource allocation problems in interference networks by differentiating variable types, leading to significant computational speed-ups and improved numerical stability.

## Contribution

The authors develop the SIT algorithm that exploits variable convexity, introduces {}-essential feasibility, and handles fractional objectives without Dinkelbach's method, outperforming existing algorithms.

## Key findings

- Achieves four orders of magnitude faster computation than state-of-the-art methods.
- Provides a robust approach to non-convex resource allocation with better numerical stability.
- Effectively handles fractional objectives without iterative Dinkelbach's algorithm.

## Abstract

Many resource allocation tasks are challenging global (i.e., non-convex) optimization problems. The main issue is that the computational complexity of these problems grows exponentially in the number of variables instead of polynomially as for many convex optimization problems. However, often the non-convexity stems only from a subset of variables. Conventional global optimization frameworks like monotonic optimization or DC programming treat all variables as global variables and require complicated, problem specific decomposition approaches to exploit the convexity in some variables. To overcome this challenge, we develop an easy-to-use algorithm that inherently differentiates between convex and non-convex variables, preserving the low computational complexity in the number of convex variables. Another issue with these widely used frameworks is that they may suffer from severe numerical problems. We discuss this issue in detail and provide a clear motivating example. The solution to this problem is to replace the traditional approach of finding an {\epsilon}-approximate solution by the novel concept of {\epsilon}-essential feasibility. The underlying algorithmic approach is called successive incumbent transcending (SIT) algorithm and builds the foundation of our developed algorithm. A further highlight of this algorithm is that it inherently treats fractional objectives making the use of Dinkelbach's iterative algorithm obsolete. Numerical experiments show a speed-up of four orders of magnitude over state-of-the-art algorithms and almost three orders of magnitude of additional speed-up over Dinkelbach's algorithm for fractional programs.