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Low‐complexity minimization algorithms
Author(s) -
Di Fiore Carmine,
Fanelli Stefano,
Zellini Paolo
Publication year - 2005
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.449
Subject(s) - hessian matrix , algorithm , broyden–fletcher–goldfarb–shanno algorithm , mathematics , minification , matrix (chemical analysis) , convergence (economics) , scheme (mathematics) , rate of convergence , mathematical optimization , computational complexity theory , exploit , computer science , mathematical analysis , channel (broadcasting) , computer network , materials science , computer security , economics , composite material , economic growth
Structured matrix algebras ℒ and a generalized BFGS‐type iterative scheme have been recently investigated to introduce low‐complexity quasi‐Newton methods, named ℒQN, for solving general (non‐structured) minimization problems. In this paper we introduce the ℒ k QN methods, which exploit ad hoc algebras at each step. Since the structure of the updated matrices can be modified at each iteration, the new methods can better fit the Hessian matrix, thereby improving the rate of convergence of the algorithm. Copyright © 2005 John Wiley & Sons, Ltd.