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

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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

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10.1016/j.laa.2015.01.010

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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",

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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

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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

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