Adaptive matrix algebras in unconstrained minimization

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}
}

Keywords: Unconstrained minimization Quasi-Newton methods Matrix algebras Iterative methods