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Path-Following Methods for Linear Programming
Abstract
In this paper a unified treatment of algorithms is described for linear programming methods based on the central path. This path is a curve along which the cost decreases, and that stays always far from the boundary of the feasible set. Several parameterizations of this curve are described in primal and primal-dual problems, and it is shown how different algorithms are obtained by following the curve using different parameterizations. Polynomial algorithms are obtained by following the curve approximately, and this concept becomes precise by using explicit rules for measuring the proximity of a point in relation to the central path.
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Cited by
A trust region method based on interior point techniques for nonlinear programming
Byrd, R. H., Gilbert, J. C., & Nocedal, J. (2000) · Mathematical Programming · doi:10.1007/pl00011391 · Cited by 1,638
Disciplined Convex Programming
Grant, M., Boyd, S., & Ye, Y. (2006) · Nonconvex Optimization and Its Applications · doi:10.1007/0-387-30528-9_7 · Cited by 1,026
Interior Methods for Nonlinear Optimization
Forsgren, A., Gill, P. E., & Wright, M. H. (2002) · SIAM Review · doi:10.1137/s0036144502414942 · Cited by 699
Metadata
- Authors
- Gonzaga, C. C.
- Venue
- SIAM Review
- Published
- 1992-06
- Volume
- 34
- Issue
- 2
- Pages
- 167-224
- ISSN
- 0036-1445 (ISSN-L)
- 1095-7200
- OpenAlex
- W2036622774
- Cited by
- 341
- References
- 0
- FWCI
- 20.20
- Type
- journal article
- Language
- en
- Open access
- closed
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- Gonzaga, C. C. (1992). Path-Following Methods for Linear Programming. SIAM Review. https://doi.org/10.1137/1034048
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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.
