Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-12-04T10:06:15.910Z Has data issue: false hasContentIssue false
  • English
  • Français

An interior point method for linear programming

Published online by Cambridge University Press:  17 February 2009

M. R. Osborne
M. R. Osborne
Affiliation:
Statistics Research Section, School of Mathematical Sciences, Australian National University, Box 4, GPO, Canberra, A. C. T. 2601, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Design of an interior point method for linear programming is discussed, and results of a simulation study reported. Emphasis is put on guessing the optimal vertex at as early a stage as possible.

Type
Research Article
Information
The ANZIAM Journal , Volume 31 , Issue 4 , April 1990 , pp. 367 - 378
Copyright
Copyright © Australian Mathematical Society 1990

References

[1] Barmes, E. R., “A variation on Karmarkar's algorithm for solving linear programming problems”, Math. Prog. 36 (1986) 174–182.CrossRefGoogle Scholar
[2] Brophy, J. F. and Smith, P. W., “Prototyping Karmarkar's algorithm using MATH/PROTRAN”, IMSL Directions 5 (1988) 2–3.Google Scholar
[3] Gay, D. M., “A variant of Karmarkar's linear programming algorithm for problems in standard form”, Math. Prog. 37 (1987) 81–90.CrossRefGoogle Scholar
[4] Karmarkar, N., “A new polynomial-time algorithm for linear programming”, Combinatorica 4 (1984) 373–395.Google Scholar
[5] Osborne, M. R., “Dual barrier functions with superfast rates of convergence for the linear programming problem”, J. Austral. Math. Soc. Ser. B 29 (1987) 39–58.Google Scholar
[6]Osborne, M. R., Finite algorithms in Optimization and Data Analysis (John Wiley, Chichester,“ 1986).Google Scholar
[7] Renegar, J., “A polynomial-time algorithm, based on Newton's method, for linear programming”, Math. Prog. 40 (1988) 59–93.Google Scholar
[8] Ye, Y. and Kojima, M., “Researching optimal dual solutions in Karmarkar's polynomial algorithm for linear programming,” Math. Prog. 39 (1987) 305–317.Google Scholar