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Generalizations of the limited-memory BFGS method based on the quasi-product form of update

  1. 1.
    0381640 - ÚI 2013 RIV NL eng J - Článek v odborném periodiku
    Vlček, Jan - Lukšan, Ladislav
    Generalizations of the limited-memory BFGS method based on the quasi-product form of update.
    Journal of Computational and Applied Mathematics. Roč. 241, 15 March (2013), s. 116-129. ISSN 0377-0427. E-ISSN 1879-1778
    Grant CEP: GA ČR GA201/09/1957
    Výzkumný záměr: CEZ:AV0Z10300504
    Klíčová slova: unconstrained minimization * variable metric methods * limited-memory methods * Broyden class updates * global convergence * numerical results
    Kód oboru RIV: BA - Obecná matematika
    Impakt faktor: 1.077, rok: 2013

    Two families of limited-memory variable metric or quasi-Newton methods for unconstrained minimization based on quasi-product form of update are derived. As for the first family, four variants how to utilize the Strang recurrences for the Broyden class of variable metric updates are investigated; three of them use the same number of stored vectors as the limited- memory BFGS method. Moreover, one of the variants does not require any additional matrix by vector multiplication. The second family uses vectors from the preceding iteration to construct a new class of variable metric updates. Resulting methods again require neither any additional matrix by vector multiplication nor any additional stored vector. Global convergence of four of presented methods is established for convex sufficiently smooth functions. Numerical results indicate that two of the new methods can save computational time substantially for certain problems.
    Trvalý link: http://hdl.handle.net/11104/0212062

     
     
Počet záznamů: 1  

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