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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F13%3A00381640" target="_blank" >RIV/67985807:_____/13:00381640 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.cam.2012.09.027" target="_blank" >http://dx.doi.org/10.1016/j.cam.2012.09.027</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.cam.2012.09.027" target="_blank" >10.1016/j.cam.2012.09.027</a>

Result language
angličtina
Original language name
Generalizations of the limited-memory BFGS method based on the quasi-product form of update
Original language description
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 ofvariable 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 methodsis established for convex sufficiently smooth functions. Numerical results indicate that two of the new methods can save computational time substantially for certain problems.
Czech name
—
Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GA201%2F09%2F1957" target="_blank" >GA201/09/1957: Development of methods for solving large scale nonlinear programming and nonsmooth optimization problems</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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