In this paper a new class of quasi-Newton methods, named LQN, is introduced in order to solve unconstrained minimization problems. The novel approach, which generalizes classical BFGS methods, is based on a Hessian updating formula involving an algebra L of matrices simultaneously diagonalized by a fast unitary transform. The complexity per step of LQN methods is O(n log_2 n), thereby improving considerably BFGS computational efficiency. Moreover, since LQN's iterative scheme utilizes single-indexed arrays, only O(n) memory allocations are required. Global convergence properties are investigated. In particular a global convergence result is obtained under suitable assumptions on f. Numerical experiences [7] confirm that LQN methods are particularly recommended for large scale problems.

DI FIORE, C., Fanelli, S., Lepore, F., Zellini, P. (2003). Matrix algebras in Quasi-Newton methods for unconstrained minimization. NUMERISCHE MATHEMATIK, 94, 479-500 [10.1007/s00211-002-0410-4].

Matrix algebras in Quasi-Newton methods for unconstrained minimization

DI FIORE, CARMINE;FANELLI, STEFANO;ZELLINI, PAOLO
2003-01-01

Abstract

In this paper a new class of quasi-Newton methods, named LQN, is introduced in order to solve unconstrained minimization problems. The novel approach, which generalizes classical BFGS methods, is based on a Hessian updating formula involving an algebra L of matrices simultaneously diagonalized by a fast unitary transform. The complexity per step of LQN methods is O(n log_2 n), thereby improving considerably BFGS computational efficiency. Moreover, since LQN's iterative scheme utilizes single-indexed arrays, only O(n) memory allocations are required. Global convergence properties are investigated. In particular a global convergence result is obtained under suitable assumptions on f. Numerical experiences [7] confirm that LQN methods are particularly recommended for large scale problems.
2003
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/08 - ANALISI NUMERICA
English
Con Impact Factor ISI
DI FIORE, C., Fanelli, S., Lepore, F., Zellini, P. (2003). Matrix algebras in Quasi-Newton methods for unconstrained minimization. NUMERISCHE MATHEMATIK, 94, 479-500 [10.1007/s00211-002-0410-4].
DI FIORE, C; Fanelli, S; Lepore, F; Zellini, P
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/14681
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