The DOI matches its Crossref record; 11 of the 11 references it cites were found in a registry or an index.
A Nonmonotone Line Search Technique for Newton’s Method
Abstract
In this paper a nonmonotone steplength selection rule for Newton’s method is proposed, which can be viewed as a generalization of Armijo’s rule. Numerical results are reported which indicate that the proposed technique may allow a considerable saving both in the number of line searches and in the number of function evaluations.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Numerical Methods for Unconstrained Optimization and Nonlinear Equations
Dennis, J. E., & Schnabel, R. B. (1996) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611971200 · Cited by 7,615
Practical Methods of Optimization
Fletcher, R. (2000) · Wiley eBooks · doi:10.1002/9781118723203 · Cited by 7,605
Iterative Solution of Nonlinear Equations in Several Variables
Ortega, J. M., & Rheinboldt, W. C. (2000) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9780898719468 · Cited by 6,860
A Rapidly Convergent Descent Method for Minimization
Fletcher, R., & Powell, M. J. D. (1963) · The Computer Journal · doi:10.1093/comjnl/6.2.163 · Cited by 4,583
Iterative Solution of Nonlinear Equations in Several Variables
I., E., Ortega, J. M., & Rheinboldt, W. C. (1971) · Mathematics of Computation · doi:10.2307/2004942 · Cited by 4,408
Constrained Optimization and Lagrange Multiplier Methods
(1982) · Elsevier eBooks · doi:10.1016/c2013-0-10366-2 · Cited by 4,016
An Automatic Method for Finding the Greatest or Least Value of a Function
Rosenbrock, H. H. (1960) · The Computer Journal · doi:10.1093/comjnl/3.3.175 · Cited by 2,957
Minimization of functions having Lipschitz continuous first partial derivatives
Armijo, L. (1966) · Pacific Journal of Mathematics · doi:10.2140/pjm.1966.16.1 · Cited by 1,983
Zimmermann, H. (1979) · European Journal of Operational Research · doi:10.1016/0377-2217(79)90240-6 · Cited by 698
The watchdog technique for forcing convergence in algorithms for constrained optimization
Chamberlain, R. M., Powell, M. J. D., Lemarechal, C., & Pedersen, H. C. (1982) · Mathematical Programming Studies · doi:10.1007/bfb0120945 · Cited by 313
Cited by
Sequential quadratic programming
Boggs, P. T., & Tolle, J. W. (1995) · Acta Numerica · doi:10.1017/s0962492900002518 · Cited by 1,858
Deformable medical image registration: a survey
Sotiras, A., Davatzikos, C., & Paragios, N. (2013) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2013.2265603 · Cited by 1,587
“Other line strategies include keeping the step size fixed, monotone line search [402], line search and golden”
BackgroundAn efficient augmented Lagrangian method with applications to total variation minimization
Li, C., Yin, W., Jiang, H., & Zhang, Y. (2013) · Computational Optimization and Applications · doi:10.1007/s10589-013-9576-1 · Cited by 656
A scaled gradient projection method for constrained image deblurring
Bonettini, S., Zanella, R., & Zanni, L. (2009) · Inverse Problems · doi:10.1088/0266-5611/25/1/015002 · Cited by 254
PETSc/TAO Users Manual (Rev. 3.19)
Argonne National Laboratory (ANL), A., Balay, S., USDOE Office of Science (SC), A. S. C. R. (., Abhyankar, S., Adams, M., Benson, S., Brown, J., Brune, P., Buschelman, K., Constantinescu, E., et al. (2023) · doi:10.2172/1968587 · Cited by 67
Metadata
- Authors
- Grippo, L., Lampariello, F., & Lucidi, S.
- Venue
- SIAM Journal on Numerical Analysis
- Published
- 1986-08
- Volume
- 23
- Issue
- 4
- Pages
- 707-716
- ISSN
- 0036-1429 (ISSN-L)
- 1095-7170
- OpenAlex
- W2043430160
- Cited by
- 1,156
- References
- 11
- FWCI
- 1.86
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: A Nonmonotone Line Search Technique for Newton’s Method. https://app.cochat.ai/papers/10.1137/0723046
- The paper
- Grippo, L., Lampariello, F., & Lucidi, S. (1986). A Nonmonotone Line Search Technique for Newton’s Method. SIAM Journal on Numerical Analysis. https://doi.org/10.1137/0723046
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
