A Unified Framework for Robust and Numerically Stable BFGS Methods with Applications in Mobile Localization

This paper presents a comprehensive unified framework that addresses the fundamental limitations of classical BFGS methods in unconstrained nonlinear optimization. We synergistically integrate Yang's robust BFGS approach with Gill and Runnoe's factored self-scaled BFGS methodology, resulting in the RFSS-BFGS algorithm. The proposed framework is rigorously evaluated through practical mobile localization based on ToA measurements. Extensive numerical experiments demonstrate that RFSS-BFGS achieves superior performance with enhanced convergence reliability and accelerated convergence rates compared to state-of-the-art variants. The algorithm provides accurate mobile localization with significantly improved positioning accuracy and computational efficiency compared to conventional approaches.

کلیدواژه ها:

BFGS ، Robust Optimization ، Global Convergence ، Mobile Localization ، Time of Arrival ، Nonlinear Optimization