The DOI matches its Crossref record; 18 of the 18 references it cites were found in a registry or an index.
Newton’s Method with a Model Trust Region Modification
Open accessAbstract
A modified Newton method for unconstrained minimization is presented and analyzed. The modification is based upon the model trust region approach. This report contains a thorough analysis of the locally constrained quadratic minimizations that arise as subproblems in the modified Newton iteration. Several promising alternatives are presented for solving these subproblems in ways that overcome certain theoretical difficulties exposed by this analysis. Very strong convergence results are presented concerning the minimization algorithm. In particular, the explicit use of second order information is justified by demonstrating that the iterates converge to a point which satisfies the second order necessary conditions for minimization. With the exception of very pathological cases this occurs whenever the algorithm is applied to problems with continuous second partial derivatives.
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
An Algorithm for Least-Squares Estimation of Nonlinear Parameters
Marquardt, D. W. (1963) · Journal of the Society for Industrial and Applied Mathematics · doi:10.1137/0111030 · Cited by 30,728
A method for the solution of certain non-linear problems in least squares
Levenberg, K. (1944) · Quarterly of Applied Mathematics · doi:10.1090/qam/10666 · Cited by 12,359
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
The algebraic eigenvalue problem
Wilkinson, J. H. (1965) · Cited by 5,833
The Levenberg-Marquardt algorithm: Implementation and theory
Moré, J. J. (1978) · Lecture Notes in Mathematics · doi:10.1007/bfb0067700 · Cited by 5,773
The Algebraic Eigenvalue Problem
I., E., & Wilkinson, J. H. (1966) · Mathematics of Computation · doi:10.2307/2003558 · Cited by 5,140
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
Introduction to matrix computations
Stewart, G. W. (1973) · International Linear Collider · Cited by 2,381
Nonlinear Programming: Sequential Unconstrained Minimization Techniques
Fiacco, A. V., & McCormick, G. P. (1968) · Defense Technical Information Center (DTIC) · Cited by 2,262
Cited by
An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds
Coleman, T. F., & Li, Y. (1996) · SIAM Journal on Optimization · doi:10.1137/0806023 · Cited by 3,320
Convex Optimization in Signal Processing and Communications
(2009) · Cambridge University Press eBooks · doi:10.1017/cbo9780511804458 · Cited by 554
Saa, P. A., & Nielsen, L. K. (2017) · Biotechnology Advances · doi:10.1016/j.biotechadv.2017.09.005 · Cited by 166
Metadata
- Authors
- Sorensen, D. C.
- Venue
- SIAM Journal on Numerical Analysis
- Published
- 1982-04
- Volume
- 19
- Issue
- 2
- Pages
- 409-426
- ISSN
- 0036-1429 (ISSN-L)
- 1095-7170
- OpenAlex
- W1979603710
- Cited by
- 560
- References
- 18
- FWCI
- 6.41
- Type
- journal article
- Language
- en
- Open access
- green
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: Newton’s Method with a Model Trust Region Modification. https://app.cochat.ai/papers/10.1137/0719026
- The paper
- Sorensen, D. C. (1982). Newton’s Method with a Model Trust Region Modification. SIAM Journal on Numerical Analysis. https://doi.org/10.1137/0719026
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.
