Název: Two limited-memory optimization methods with minimum violation of the previous quasi-Newton equations
Autoři: Vlček, Jan ; Lukšan, Ladislav
Typ dokumentu: Výzkumné zprávy
Rok: 2020
Jazyk: eng
Edice: Technical Report, svazek: V-1280
Abstrakt: Limited-memory variable metric methods based on the well-known BFGS update are widely used for large scale optimization. The block version of the BFGS update, derived by Schnabel (1983), Hu and Storey (1991) and Vlček and Lukšan (2019), satisfies the quasi-Newton equations with all used difference vectors and for quadratic objective functions gives the best improvement of convergence in some sense, but the corresponding direction vectors are not descent directions generally. To guarantee the descent property of direction vectors and simultaneously violate the quasi-Newton equations as little as possible in some sense, two methods based on the block BFGS update are proposed. They can be advantageously combined with methods based on vector corrections for conjugacy (Vlček and Lukšan, 2015). Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical experiments demonstrate the efficiency of the new methods.
Klíčová slova: global convergence; limited-memory methods; numerical results; 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: http://hdl.handle.net/11104/0310865

Trvalý odkaz NUŠL: http://www.nusl.cz/ntk/nusl-432144


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