Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
BIT Numerical Mathematics
Published in: BIT Numerical Mathematics 3/2020

13-12-2019

On monotonic estimates of the norm of the minimizers of regularized quadratic functions in Krylov spaces

Authors: Coralia Cartis, Nicholas I. M. Gould, Marius Lange

Published in: BIT Numerical Mathematics | Issue 3/2020

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We show that the minimizers of regularized quadratic functions restricted to their natural Krylov spaces increase in Euclidean norm as the spaces expand.
previous article Weak convergence rates of splitting schemes for the stochastic Allen–Cahn equation
next article Time integration of symmetric and anti-symmetric low-rank matrices and Tucker tensors

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now
Literature
1.
Bianconcini, T., Liuzzi, G., Morini, B., Sciandrone, M.: On the use of iterative methods in cubic regularization for unconstrained optimization. Comput. Optim. Appl. 60(1), 35–57 (2015)MathSciNetCrossRef
2.
3.
Cartis, C., Gould, N.I.M., Toint, PhL: Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results. Math. Program. Ser. A 127(2), 245–295 (2011)MathSciNetCrossRef
4.
Conn, A.R., Gould, N.I.M., Toint, PhL: Trust-Region Methods. SIAM, Philadelphia (2000)CrossRef
5.
Gould, N.I.M., Robinson, D.P., Thorne, H.S.: On solving trust-region and other regularised subproblems in optimization. Math. Program. Comput. 2(1), 21–57 (2010)MathSciNetCrossRef
6.
7.
Griewank, A.: The modification of Newton’s method for unconstrained optimization by bounding cubic terms. Technical Report NA/12, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England (1981)
8.
Kohler, J.M., Lucchi, A.: Sub-sampled cubic regularization for non-convex optimization. In: Precup, D., Teh, Y.W., (eds.) Proceedings of the 34th International Conference on Machine Learning, volume 70 of Proceedings of Machine Learning Research, pp. 1895–1904 (2017)
9.
Lange, M.: Subproblem solutions in cubic regularisation methods. M.Sc. thesis, University of Oxford, England (2017)
10.
Liesen, J., Strakoš, Z.: Krylov Subspace Methods. Oxford University Press, Oxford (2013)MATH
11.
Lukšan, L., Matonoha, C., Vlček, J.: On Lagrange multipliers of trust-region subproblems. BIT 48(4), 763–768 (2008)MathSciNetCrossRef
12.
13.
Steihaug, T.: The conjugate gradient method and trust regions in large scale optimization. SIAM J. Numer. Anal. 20(3), 626–637 (1983)MathSciNetCrossRef
Metadata
Title
On monotonic estimates of the norm of the minimizers of regularized quadratic functions in Krylov spaces
Authors
Coralia Cartis
Nicholas I. M. Gould
Marius Lange
Publication date
13-12-2019
Publisher
Springer Netherlands
Published in
BIT Numerical Mathematics / Issue 3/2020
Print ISSN: 0006-3835
Electronic ISSN: 1572-9125
DOI
https://doi.org/10.1007/s10543-019-00791-2

Other articles of this Issue 3/2020

BIT Numerical Mathematics 3/2020 Go to the issue

OriginalPaper

Analysis of an approximation to a fractional extension problem

OriginalPaper

Mean-square convergence rates of stochastic theta methods for SDEs under a coupled monotonicity condition

OriginalPaper

Exact BDF stability angles with maple

OriginalPaper

Automated local Fourier analysis (aLFA)

OriginalPaper

Time integration of symmetric and anti-symmetric low-rank matrices and Tucker tensors

OriginalPaper

Geometrically continuous piecewise Chebyshevian NU(R)BS

Premium Partner

    Image Credits