The DOI matches its Crossref record; 31 of the 31 references it cites were found in a registry or an index.
A Convergent Incremental Gradient Method with a Constant Step Size
Abstract
An incremental aggregated gradient method for minimizing a sum of continuously differentiable functions is presented. The method requires a single gradient evaluation per iteration and uses a constant step size. For the case that the gradient is bounded and Lipschitz continuous, we show that the method visits infinitely often regions in which the gradient is small. Under certain unimodality assumptions, global convergence is established. In the quadratic case, a global linear rate of convergence is shown. The method is applied to distributed optimization problems arising in wireless sensor networks, and numerical experiments compare the new method with other incremental gradient methods.
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
Friedman, J., Hastie, T., & Tibshirani, R. (2000) · The Annals of Statistics · doi:10.1214/aos/1016218223 · Cited by 6,884
Advanced engineering mathematics
(1998) · Choice Reviews Online · doi:10.5860/choice.35-5129 · Cited by 4,100
(2012) · Encyclopedia of the Sciences of Learning · doi:10.1007/978-1-4419-1428-6_5086 · Cited by 3,515
A View of the Em Algorithm that Justifies Incremental, Sparse, and other Variants
Neal, R. M., & Hinton, G. E. (1998) · Learning in Graphical Models · doi:10.1007/978-94-011-5014-9_12 · Cited by 2,187
(1989) · Choice Reviews Online · doi:10.5860/choice.26-5109 · Cited by 1,755
Varberg, D. E. (1973) · Cited by 1,700
Distributed optimization in sensor networks
Rabbat, M., & Nowak, R. (2004) · Proceedings of the 3rd international symposium on Information processing in sensor networks · doi:10.1145/984622.984626 · Cited by 901
Sheng, X., & Hu, Y.-H. (2005) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2004.838930 · Cited by 714
Habitat monitoring with sensor networks
Szewczyk, R., Osterweil, E., Polastre, J., Hamilton, M., Mainwaring, A., & Estrin, D. (2004) · Communications of the ACM · doi:10.1145/990680.990704 · Cited by 702
Logistic Regression, AdaBoost and Bregman Distances
Collins, M., Schapire, R. E., & Singer, Y. (2002) · Machine Learning · doi:10.1023/a:1013912006537 · Cited by 687
Cited by
Constrained Consensus and Optimization in Multi-Agent Networks
Nedic, A., Ozdaglar, A., & Parrilo, P. A. (2010) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2010.2041686 · Cited by 2,086
Distributed Stochastic Subgradient Projection Algorithms for Convex Optimization
Sundhar Ram, S., Nedić, A., & Veeravalli, V. V. (2010) · Journal of Optimization Theory and Applications · doi:10.1007/s10957-010-9737-7 · Cited by 814
Fast Distributed Gradient Methods
Jakovetic, D., Xavier, J., & Moura, J. M. F. (2014) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2014.2298712 · Cited by 624
A Proximal Stochastic Gradient Method with Progressive Variance Reduction
Xiao, L., & Zhang, T. (2014) · SIAM Journal on Optimization · doi:10.1137/140961791 · Cited by 592
Sayed, A. H. (2014) · Proceedings of the IEEE · doi:10.1109/jproc.2014.2306253 · Cited by 587
Metadata
- Authors
- Blatt, D., Hero, A. O., & Gauchman, H.
- Venue
- SIAM Journal on Optimization
- Published
- 2007-01
- Volume
- 18
- Issue
- 1
- Pages
- 29-51
- ISSN
- 1052-6234 (ISSN-L)
- 1095-7189
- OpenAlex
- W1988795359
- Cited by
- 306
- References
- 31
- FWCI
- 7.88
- 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 Convergent Incremental Gradient Method with a Constant Step Size. https://app.cochat.ai/papers/10.1137/040615961
- The paper
- Blatt, D., Hero, A. O., & Gauchman, H. (2007). A Convergent Incremental Gradient Method with a Constant Step Size. SIAM Journal on Optimization. https://doi.org/10.1137/040615961
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.
