A Unified Framework for Robust and Numerically Stable BFGS Methods with Applications in Mobile Localization, By Heidar Keshavarz

Research

Title	A Unified Framework for Robust and Numerically Stable BFGS Methods with Applications in Mobile Localization
Type	Presentation
Keywords	BFGS, Robust Optimization, Global Convergence, Mobile Localization, Time of Arrival, Nonlinear Optimization.
Researchers	poria keshtkar (First researcher) , Heidar Keshavarz (Second researcher)

Abstract

This paper presents a comprehensive unified framework that addresses the fundamental limitations of classical BFGS1 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-BFGS2 algorithm.The proposed framework is rigorously evaluated through practical mobile localization based on ToA3 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.