Movatterモバイル変換


[0]ホーム

URL:


×

zbMATH Open — the first resource for mathematics

from until
Reset all

Examples

GeometrySearch for the termGeometry inany field. Queries arecase-independent.
Funct*Wildcard queries are specified by* (e .g.functions,functorial, etc.). Otherwise the search isexact.''Topological group'':Phrases (multi - words) should be set in''straight quotation marks''.
au: Bourbaki & ti: AlgebraSearch forauthorBourbaki andtitleAlgebra. Theand-operator & is default and can be omitted.
Chebyshev | TschebyscheffTheor-operator| allows to search forChebyshev orTschebyscheff.
Quasi* map* py: 1989The resulting documents havepublicationyear1989.
so:Eur* J* Mat* Soc* cc:14Search for publications in a particularsource with aMathematics SubjectClassificationcode in14.
cc:*35 ! any:ellipticSearch for documents about PDEs (prefix with * to search only primary MSC); the not-operator ! eliminates all results containing the wordelliptic.
dt: b & au: HilbertThedocumenttype is set tobooks; alternatively:j forjournal articles,a forbookarticles.
py: 2000 - 2015 cc:(94A | 11T)Numberranges when searching forpublicationyear are accepted . Terms can be grouped within( parentheses).
la: chineseFind documents in a givenlanguage .ISO 639 - 1 (opens in new tab) language codes can also be used.
st: c r sFind documents that arecited, havereferences and are from asingle author.

Fields

ab Text from the summary or review (for phrases use “. ..”)
an zbMATH ID, i.e.: preliminary ID, Zbl number, JFM number, ERAM number
any Includes ab, au, cc, en, rv, so, ti, ut
arxiv arXiv preprint number
au Name(s) of the contributor(s)
br Name of a person with biographic references (to find documents about the life or work)
cc Code from the Mathematics Subject Classification (prefix with* to search only primary MSC)
ci zbMATH ID of a document cited in summary or review
db Database: documents in Zentralblatt für Mathematik/zbMATH Open (db:Zbl), Jahrbuch über die Fortschritte der Mathematik (db:JFM), Crelle's Journal (db:eram), arXiv (db:arxiv)
dt Type of the document: journal article (dt:j), collection article (dt:a), book (dt:b)
doi Digital Object Identifier (DOI)
ed Name of the editor of a book or special issue
en External document ID: DOI, arXiv ID, ISBN, and others
in zbMATH ID of the corresponding issue
la Language (use name, e.g.,la:French, orISO 639-1, e.g.,la:FR)
li External link (URL)
na Number of authors of the document in question. Interval search with “-”
pt Reviewing state: Reviewed (pt:r), Title Only (pt:t), Pending (pt:p), Scanned Review (pt:s)
pu Name of the publisher
py Year of publication. Interval search with “-”
rft Text from the references of a document (for phrases use “...”)
rn Reviewer ID
rv Name or ID of the reviewer
se Serial ID
si swMATH ID of software referred to in a document
so Bibliographical source, e.g., serial title, volume/issue number, page range, year of publication, ISBN, etc.
st State: is cited (st:c), has references (st:r), has single author (st:s)
sw Name of software referred to in a document
ti Title of the document
ut Keywords

Operators

a & bLogical and (default)
a | bLogical or
!abLogical not
abc*Right wildcard
ab cPhrase
(ab c)Term grouping

See also ourGeneral Help.

Truncated-Newton algorithms for large-scale unconstrained optimization.(English)Zbl 0523.90078


MSC:

90C30 Nonlinear programming
49M37 Numerical methods based on nonlinear programming
65K05 Numerical mathematical programming methods
49M15 Newton-type methods

Cite

References:

[1]Axelsson, O.; Barker, V. A., Solution of linear systems of equations: Iterative methods, Sparse matrix techniques, 1-51 (1976), New York: Springer-Verlag, New York ·Zbl 0354.65021
[2]Chandra, R., Conjugate gradient methods for partial differential equations (1978), New Haven, CT: Yale University, New Haven, CT
[3]R. Chandra, S.C. Eisenstat and M.H. Schultz, “The modified conjugate residual method for partial differential equations”, in: R. Vichnevetsky, ed.,Advance in computer methods for partial differential equations II, Proceedings of the Second International Symposium on Computer Methods for Partial Differential Equations, Lehigh University, Bethlehem, PA (International Association for Mathematics and Computers in Simulation, June 1977) pp. 13-19.
[4]Curtis, A. R.; Powell, M. J.D.; Reid, J. K., On the estimation of sparse Jacobian matrices, Journal of the Institute of Mathematics and its Applications, 13, 117-119 (1974) ·Zbl 0273.65036 ·doi:10.1093/imamat/13.1.117
[5]Dembo, R. S.; Eisenstat, S. C.; Steihaug, T., Inexact Newton methods, SIAM Journal of Numerical Analysis, 19, 400-408 (1982) ·Zbl 0478.65030 ·doi:10.1137/0719025
[6]Dembo, R. S.; Klincewicz, J. G., A scaled reduced gradient algorithm for network flow problems with convex separable costs, Mathematical Programming Studies, 15, 125-147 (1981) ·Zbl 0477.90025 ·doi:10.1007/BFb0120941
[7]R. S. Dembo and T. Steihaug, “A test problem for large-scale unconstrained minimization”, School of Organization and Management, Yale University (New Haven, CT) Working Paper Series B (in preparation). ·Zbl 0559.90080
[8]Dennis, J. E. Jr.; Moré, J. J., Quasi-Newton methods, motivation and theory, SIAM Review, 19, 46-89 (1977) ·Zbl 0356.65041 ·doi:10.1137/1019005
[9]Fletcher, R.; Watson, G. A., Conjugate gradient methods for indefinite systems, Numerical Analysis, 73-89 (1976), New York: Springer-Verlag, New York ·Zbl 0326.65033 ·doi:10.1007/BFb0080116
[10]Fletcher, R., Unconstrained optimization (1980), New York: John Wiley and Sons, New York ·Zbl 0439.93001
[11]Garg, N. K.; Tapia, R. A., QDN: A variable storage algorithm for unconstrained optimization (1977), Houston, TX: Department of Mathematical Sciences, Rice University, Houston, TX
[12]P.E. Gill and W. Murray, “Safeguarded steplength algorithm for optimization using descent methods”, Technical Report NPL NA 37, National Physical Laboratory (1974).
[13]P.E. Gill, W. Murray and S.G. Nash, “A conjugate-gradient approach to Newton-type methods”, presented at ORSA/TIMS Joint National Meeting (Colorado Springs, November 1980).
[14]Gill, P. E.; Murray, W.; Wright, M. H., Practical optimization (1981), New York: Academic Press, New York ·Zbl 0503.90062
[15]Hestenes, M. R., Conjugate direction methods in optimization (1980), New York: Springer-Verlag, New York ·Zbl 0439.49001 ·doi:10.1007/978-1-4612-6048-6
[16]Hestenes, M. R.; Stiefel, E., Methods of conjugate gradients for solving linear systems, Journal of Research of the National Bureau of Standards, 49, 409-436 (1952) ·Zbl 0048.09901 ·doi:10.6028/jres.049.044
[17]Luenberger, D. G., Hyperbolic pairs in the method of conjugate gradients, SIAM Journal on Applied Mathematics, 17, 1263-1267 (1969) ·Zbl 0187.09704 ·doi:10.1137/0117118
[18]Murtagh, B.; Saunders, M., Large-scale linearly constrained optimization, Mathematical Programming, 14, 41-72 (1978) ·Zbl 0383.90074 ·doi:10.1007/BF01588950
[19]Nocedal, J., Updating Quasi-Newton matrices with limited storage, Mathematics of Computation, 35, 773-782 (1980) ·Zbl 0464.65037 ·doi:10.1090/S0025-5718-1980-0572855-7
[20]O’Leary, D. P., A discrete Newton algorithm for minimizing a function of many variables, Mathematical Programming, 23, 20-33 (1982) ·Zbl 0477.90055 ·doi:10.1007/BF01583777
[21]Ortega, J. M.; Rheinboldt, W. C., Iterative solution of nonlinear equations in several variables (1970), New York: Academic Press, New York ·Zbl 0241.65046
[22]Powell, M. J.D.; Toint, Ph. L., On the estimation of sparse Hessian matrices, SIAM Journal on Numerical Analysis, 16, 1060-1074 (1979) ·Zbl 0426.65025 ·doi:10.1137/0716078
[23]Shanno, D. F., On the convergence of a new conjugate gradient method, SIAM Journal on Numerical Analysis, 15, 1247-1257 (1978) ·Zbl 0408.90071 ·doi:10.1137/0715085
[24]Shanno, D. F.; Phua, K. H., Algorithm 500: Minimization of unconstrained multivariate functions, Transactions on Mathematical Software, 2, 87-94 (1976) ·Zbl 0319.65042 ·doi:10.1145/355666.355673
[25]Steihaug, T., Quasi-Newton methods for large scale nonlinear problems (1980), New Haven, CT: Yale University, New Haven, CT
[26]Toint, Ph. L., Some numerical results using a sparse matrix updating formula in unconstrained optimization, Mathematics of Computation, 32, 839-851 (1978) ·Zbl 0381.65036 ·doi:10.1090/S0025-5718-1978-0483452-7
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
© 2025FIZ Karlsruhe GmbHPrivacy PolicyLegal NoticesTerms & Conditions
  • Mastodon logo
 (opens in new tab)

[8]ページ先頭

©2009-2025 Movatter.jp