Application of the infinitely many times repeated BNS update and conjugate directions to limited-memory optimization methods

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dc.contributor.authorVlček, Jan
dc.contributor.authorLukšan, Ladislav
dc.date.accessioned2020-10-23T06:14:00Z
dc.date.available2020-10-23T06:14:00Z
dc.date.issued2019
dc.description.abstractTo improve the performance of the L-BFGS method for large scale unconstrained optimization, repeating of some BFGS updates was proposed e.g. in [1]. Since this can be time consuming, the extra updates need to be selected carefully. We show that groups of these updates can be repeated infinitely many times under some conditions, without a noticeable increase of the computational time; the limit update is a block BFGS update [17]. It can be obtained by solving of some Lyapunov matrix equation whose order can be decreased by application of vector corrections for conjugacy [16]. Global convergence of the proposed algorithm is established for convex and sufficiently smooth functions. Numerical results indicate the efficiency of the new method.cs
dc.format.extent10 strancs
dc.identifier.doi10.21136/panm.2018.19
dc.identifier.urihttps://dspace.tul.cz/handle/15240/158022
dc.identifier.urihttps://dml.cz/handle/10338.dmlcz/703083
dc.language.isocscs
dc.publisherACAD SCIENCES CZECH REPUBLIC, INST MATHEMATICS, ZITNA 25, PRAHA 1, CZ-115 67, CZECH REPUBLIC
dc.relation.ispartofPROGRAMS AND ALGORITHMS OF NUMERICAL MATHEMATICS 19
dc.subjectnumerical resultscs
dc.subjectglobal convergencecs
dc.subjectthe conjugate directionscs
dc.subjectthe Lyapunov matrix equationcs
dc.subjectthe repeated Byrd-Nocedal-Schnabel updatecs
dc.subjectlimited-memory variable metric methodscs
dc.subjectUnconstrained minimizationcs
dc.titleApplication of the infinitely many times repeated BNS update and conjugate directions to limited-memory optimization methodscs
dc.typeProceedings Paper
local.citation.epage185
local.citation.spage177
local.event.edate2018-06-29
local.event.locationInt Ctr Spiritual Rehabilitat, Hejnice, CZECH REPUBLIC
local.event.sdate2018-06-24
local.event.title19th Conference on Programs and Algorithms of Numerical Mathematics (PANM)
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