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On Minimizing a Convex Function Subject to Linear Inequalities
Abstract
Summary: The minimization of a convex function of variables subject to linear inequalities is discussed briefly in general terms. Dantzig’s Simplex Method is extended to yield finite algorithms for minimizing either a convex quadratic function or the sum of the t largest of a set of linear functions, and the solution of a generalization of the latter problem is indicated. In the last two sections a form of linear programming with random variables as coefficients is described, and shown to involve the minimization of a convex function.
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Cited by
Management Models and Industrial Applications of Linear Programming
Charnes, A., & Cooper, W. W. (1957) · Management Science · doi:10.1287/mnsc.4.1.38 · Cited by 1,902
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AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients
Zhuang, J., Tang, T., Ding, Y., Tatikonda, S., Dvornek, N., Papademetris, X., & Duncan, J. S. (2020) · arXiv · doi:10.48550/arxiv.2010.07468 · Cited by 382
A multivariate analogue of the one-sided test
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Metadata
- Authors
- Beale, E. M. L.
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 1955-07-01
- Volume
- 17
- Issue
- 2
- Pages
- 173-184
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W2502170570
- Cited by
- 625
- References
- 0
- FWCI
- 2.49
- Type
- journal article
- Language
- en
- Open access
- closed
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- Beale, E. M. L. (1955). On Minimizing a Convex Function Subject to Linear Inequalities. Journal of the Royal Statistical Society Series B: Statistical Methodology. https://doi.org/10.1111/j.2517-6161.1955.tb00191.x
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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.
