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A limited-memory optimization method using the infinitely many times repeated BNS update and conjugate directions

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24220%2F19%3A00009689" target="_blank" >RIV/46747885:24220/19:00009689 - isvavai.cz</a>

  • Alternative codes found

    RIV/67985807:_____/19:00497050

  • Result on the web

    <a href="https://www.sciencedirect.com/science/article/pii/S0377042718306629" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0377042718306629</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1016/j.cam.2018.10.054" target="_blank" >10.1016/j.cam.2018.10.054</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    A limited-memory optimization method using the infinitely many times repeated BNS update and conjugate directions

  • Original language description

    To improve the performance of the limited-memory variable metric L-BFGS method for large scale unconstrained optimization, repeating of some BFGS updates was proposed e.g. in Al-Baali (1999, 2002). Since the repeating process can be time consuming, the suitable extra updates need to be selected carefully. We show that for the limited-memory variable metric BNS method, matrix updating can be efficiently repeated infinitely many times under some conditions, with only a small increase of the number of arithmetic operations. The limit matrix can be written as a block BFGS update (Vlcek and Luksan, 2018), which can be obtained by solving of some low-order Lyapunov matrix equation. The resulting method can be advantageously combined with methods based on vector corrections for conjugacy, see e.g. Vlcek and Luksan (2015). Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical experiments demonstrate the efficiency of the new method.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10102 - Applied mathematics

Result continuities

  • Project

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2019

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Journal of Computational and Applied Mathematics

  • ISSN

    0377-0427

  • e-ISSN

  • Volume of the periodical

    351

  • Issue of the periodical within the volume

    MAY

  • Country of publishing house

    NL - THE KINGDOM OF THE NETHERLANDS

  • Number of pages

    15

  • Pages from-to

    14-28

  • UT code for WoS article

    000468555100003

  • EID of the result in the Scopus database

    2-s2.0-85057130621