The DOI matches its Crossref record.
On Nonlinear Fractional Programming
Abstract
The main purpose of this paper is to delineate an algorithm for fractional programming with nonlinear as well as linear terms in the numerator and denominator. The algorithm presented is based on a theorem by Jagannathan (Jagannathan, R. 1966. On some properties of programming problems in parametric form pertaining to fractional programming. Management Sci. 12 609–615.) concerning the relationship between fractional and parametric programming. This theorem is restated and proved in a somewhat simpler way. Finally, it is shown how the given algorithm can be related to the method of Isbell and Marlow (Isbell, J. R., W. H. Marlow. 1956. Attrition games. Naval Res. Logist. Quart. 3 71–93.) for linear fractional programming and to the quadratic parametric approach by Ritter (Ritter, K. 1962. Ein Verfahren zur Lösung parameterabhängiger, nichtlinearer Maximum- Probleme. Unternehmensforschung, Band 6, S. 149–166.). The Appendix contains a numerical example.
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
Cited by
Fisher, A., Rudin, C., & Dominici, F. (2018) · arXiv · doi:10.48550/arxiv.1801.01489 · Cited by 1,165
Energy Efficient Federated Learning Over Wireless Communication Networks
Yang, Z., Chen, M., Saad, W., Hong, C. S., & Shikh-Bahaei, M. (2021) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2020.3037554 · Cited by 1,153
A Fast Parametric Maximum Flow Algorithm and Applications
Gallo, G., Grigoriadis, M. D., & Tarjan, R. E. (1989) · SIAM Journal on Computing · doi:10.1137/0218003 · Cited by 427
Delay Minimization for NOMA-MEC Offloading
Ding, Z., Ng, D. W. K., Schober, R., & Poor, H. V. (2018) · IEEE Signal Processing Letters · doi:10.1109/lsp.2018.2876019 · Cited by 189
Energy Efficiency Optimization With SWIPT in MIMO Broadcast Channels for Internet of Things
Tang, J., So, D. K. C., Zhao, N., Shojaeifard, A., & Wong, K.-K. (2018) · IEEE Internet of Things Journal · doi:10.1109/jiot.2017.2785861 · Cited by 109
Metadata
- Authors
- Dinkelbach, W.
- Venue
- Management Science
- Published
- 1967-03
- Volume
- 13
- Issue
- 7
- Pages
- 492-498
- ISSN
- 0025-1909 (ISSN-L)
- 1526-5501
- OpenAlex
- W1967956032
- Cited by
- 3,139
- References
- 0
- FWCI
- 2.05
- 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: On Nonlinear Fractional Programming. https://app.cochat.ai/papers/10.1287/mnsc.13.7.492
- The paper
- Dinkelbach, W. (1967). On Nonlinear Fractional Programming. Management Science. https://doi.org/10.1287/mnsc.13.7.492
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.
