Abstract
In this paper we study adaptive $L(k)QN$ methods, involving special matrix algebras of low complexity, to solve general (non-structured) unconstrained minimization problems. These methods, which generalize the classical BFGS method, are based on an iterative formula which exploits, at each step, an ad hoc chosen matrix algebra $L(k)$. A global convergence result is obtained under suitable assumptions on $f$.
Please cite this work as:
@article{cipolla2015adaptive,
title={Adaptive matrix algebras in unconstrained minimization},
author={Cipolla, Stefano and Di Fiore, Carmine and Tudisco, Francesco and Zellini, Paolo},
journal={Linear Algebra and its Applications},
volume={471},
pages={544--568},
year={2015},
publisher={Elsevier}
}