Název: Some modifications of the limited-memory variable metric optimization methods
Autoři: Vlček, Jan ; Lukšan, Ladislav
Typ dokumentu: Výzkumné zprávy
Rok: 2023
Jazyk: eng
Edice: Technical Report, svazek: V-1290
Abstrakt: Several modifications of the limited-memory variable metric (or quasi-Newton) line search methods for large scale unconstrained optimization are investigated. First the block version of the symmetric rank-one (SR1) update formula is derived in a similar way as for the block BFGS update in Vlˇcek and Lukˇsan (Numerical Algorithms 2019). The block SR1 formula is then modified to obtain an update which can reduce the required number of arithmetic operations per iteration. Since it usually violates the corresponding secant conditions, this update is combined with the shifting investigated in Vlˇcek and Lukˇsan (J. Comput. Appl. Math. 2006). Moreover, a new efficient way how to realize the limited-memory shifted BFGS method is proposed. For a class of methods based on the generalized shifted economy BFGS update, global convergence is established. A numerical comparison with the standard L-BFGS and BNS methods is given.
Klíčová slova: arithmetic operations reduction; global convergence; limited-memory methods; unconstrained minimization; variable metric methods; variationally derived methods
Práva: Dílo je chráněno podle autorského zákona č. 121/2000 Sb.

Instituce: Ústav informatiky AV ČR (web)
Původní záznam: https://hdl.handle.net/11104/0338248

Trvalý odkaz NUŠL: http://www.nusl.cz/ntk/nusl-519915


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