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.