Adaptive matrix algebras in unconstrained minimization

Stefano Cipolla; Carmine Di Fiore; Francesco Tudisco; Paolo Zellini

doi:10.1016/j.laa.2015.01.010

Adaptive matrix algebras in unconstrained minimization

Stefano Cipolla, Carmine Di Fiore, Francesco Tudisco, Paolo Zellini

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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.

Original language	English
Pages (from-to)	544-568
Number of pages	25
Journal	Linear Algebra and its Applications
Volume	471
DOIs	https://doi.org/10.1016/j.laa.2015.01.010
Publication status	Published - 30 Jan 2015

Keywords

unconstrained minimisation
unconstrained minimization
quasi-Newton BFGS method
matrix algebras
iterative algorithm
convergence

Access to Document

10.1016/j.laa.2015.01.010

Cite this

@article{2e0602c9b0bf42ac87eab74f3e194c4d,

title = "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.",

keywords = "unconstrained minimisation, unconstrained minimization, quasi-Newton BFGS method, matrix algebras, iterative algorithm, convergence",

author = "Stefano Cipolla and {Di Fiore}, Carmine and Francesco Tudisco and Paolo Zellini",

year = "2015",

month = jan,

day = "30",

doi = "10.1016/j.laa.2015.01.010",

language = "English",

volume = "471",

pages = "544--568",

journal = "Linear Algebra and its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

}

TY - JOUR

T1 - Adaptive matrix algebras in unconstrained minimization

AU - Cipolla, Stefano

AU - Di Fiore, Carmine

AU - Tudisco, Francesco

AU - Zellini, Paolo

PY - 2015/1/30

Y1 - 2015/1/30

N2 - 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.

AB - 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.

KW - unconstrained minimisation

KW - unconstrained minimization

KW - quasi-Newton BFGS method

KW - matrix algebras

KW - iterative algorithm

KW - convergence

U2 - 10.1016/j.laa.2015.01.010

DO - 10.1016/j.laa.2015.01.010

M3 - Article

SN - 0024-3795

VL - 471

SP - 544

EP - 568

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -

Adaptive matrix algebras in unconstrained minimization

Abstract

Keywords

Access to Document

Fingerprint

Cite this