The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
Linear Programming
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“As this function is linear in κi, optimization subject to the saddle-node constraints equations (2) and (3) is equivalent to a Linear Programming (LP) problem40,41:4”
From Shaping the topology of folding pathways in mechanical systems (2018) · cites this paper as [41]
Citations
Cites
A new polynomial-time algorithm for linear programming
Karmarkar, N. (1984) · Combinatorica · doi:10.1007/bf02579150 · Cited by 4,794
Activity Analysis of Production and Allocation.
Carter, C. F., & Koopmans, T. C. (1952) · The Economic Journal · doi:10.2307/2226909 · Cited by 1,934
Programming of Interdependent Activities: II Mathematical Model
Dantzig, G. B. (1949) · Econometrica · doi:10.2307/1905523 · Cited by 216
Research works printed but not linked: 2
- Kantorovich, L.: A new method of solving some classes of extremal problems. Dokl. Akad. Sci. USSR 28, 211–214 (1940)
- Klee, V., Minty, G.: How good is the simplex algorithm? In: Shisha, O. (ed.) Inequalities–III, pp. 159–175. Academic, New York (1972)
Cited by
Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithms
Zhang, K., Yang, Z., & Başar, T. (2021) · Studies in Systems, Decision and Control · doi:10.1007/978-3-030-60990-0_12 · Cited by 1,264
SCDC: bulk gene expression deconvolution by multiple single-cell RNA sequencing references
Dong, M., Thennavan, A., Urrutia, E., Li, Y., Perou, C. M., Zou, F., & Jiang, Y. (2021) · Briefings in Bioinformatics · doi:10.1093/bib/bbz166 · Cited by 252
Verisig: verifying safety properties of hybrid systems with neural network controllers
Ivanov, R., Weimer, J., Alur, R., Pappas, G. J., & Lee, I. (2019) · Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control · doi:10.1145/3302504.3311806 · Cited by 216
Fundamental Limits to the Refractive Index of Transparent Optical Materials
Shim, H., Monticone, F., & Miller, O. D. (2021) · Advanced Materials · doi:10.1002/adma.202103946 · Cited by 94
Morphological Perceptrons: Geometry and Training Algorithms
Charisopoulos, V., & Maragos, P. A. (2017) · Lecture notes in computer science · doi:10.1007/978-3-319-57240-6_1 · Cited by 59
Metadata
- Authors
- Vanderbei, R. J.
- Affiliations
- Princeton University (US)
- Corresponding author
- Vanderbei, Robert J.
- ORCID
- Vanderbei, Robert J.
- Venue
- Encyclopedia of Applied and Computational Mathematics
- Publisher
- Springer Berlin Heidelberg
- Published
- 2015
- Pages
- 796-800
- OpenAlex
- W4249841832
- Cited by
- 27
- References
- 3
- Citations by year
- 2026: 3 · 2025: 1 · 2024: 1 · 2022: 2 · 2021: 6 · 2020: 4 · 2019: 4 · 2018: 3 · 2017: 3
- Type
- reference entry
- Language
- en
- Open access
- closed
- Licence
- www.springernature.com/gp/researchers/text-and-data-mining (tdm)
- www.springernature.com/gp/researchers/text-and-data-mining (vor)
- Locations
- Springer eBooks (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Numerical Analysis › Advanced Optimization Algorithms Research
- Social Sciences › Decision Sciences › Management Science and Operations Research › Optimization and Mathematical Programming
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Complexity and Algorithms in Graphs
- Keywords
- linear programming, optimization theory, convex analysis
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: Linear Programming. https://app.cochat.ai/papers/10.1007/978-3-540-70529-1_419
- The paper
- Vanderbei, R. J. (2015). Linear Programming. Encyclopedia of Applied and Computational Mathematics. https://doi.org/10.1007/978-3-540-70529-1_419
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.
