The DOI matches its Crossref record.
Fractional Programming. II, On Dinkelbach's Algorithm
Abstract
Dinkelbach's algorithm [Dinkelbach, W. 1967. On nonlinear fractional programming. Management Sci. 13 492–498.] solving the parametric equivalent of a fractional program is investigated. It is shown that the algorithm converges superlinearly and often (locally) quadratically. A priori and a posteriori error estimates are derived. Using those estimates and duality as introduced in Part I, a revised version of the algorithm is proposed. In addition, a similar algorithm is presented where, in contrast to Dinkelbach's procedure, the rate of convergence is still controllable. Error estimates are derived also for this algorithm.
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
Energy Efficiency in Wireless Networks via Fractional Programming Theory
Zappone, A., & Jorswieck, E. (2015) · Foundations and Trends in Communications and Information Theory · doi:10.1561/0100000088 · Cited by 513
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
Multi-Level Over-the-Air Aggregation of Mobile Edge Computing Over D2D Wireless Networks
Wang, F., & Lau, V. K. N. (2022) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2022.3165658 · Cited by 21
Metadata
- Authors
- Schaible, S.
- Venue
- Management Science
- Published
- 1976-04
- Volume
- 22
- Issue
- 8
- Pages
- 868-873
- ISSN
- 0025-1909 (ISSN-L)
- 1526-5501
- OpenAlex
- W1999218360
- Cited by
- 246
- References
- 0
- FWCI
- 1.10
- 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: Fractional Programming. II, On Dinkelbach's Algorithm. https://app.cochat.ai/papers/10.1287/mnsc.22.8.868
- The paper
- Schaible, S. (1976). Fractional Programming. II, On Dinkelbach's Algorithm. Management Science. https://doi.org/10.1287/mnsc.22.8.868
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.
