Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-25T06:48:43.974Z Has data issue: false hasContentIssue false
  • English
  • Français

A SELF-REGULAR NEWTON BASED ALGORITHM FOR LINEAR OPTIMIZATION

Published online by Cambridge University Press:  05 February 2010

M. SALAHI
M. SALAHI*
Affiliation:
Department of Mathematics, University of Guilan, Rasht, Iran (email: [email protected], [email protected])
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.

In this paper, using the framework of self-regularity, we propose a hybrid adaptive algorithm for the linear optimization problem. If the current iterates are far from a central path, the algorithm employs a self-regular search direction, otherwise the classical Newton search direction is employed. This feature of the algorithm allows us to prove a worst case iteration bound. Our result matches the best iteration bound obtained by the pure self-regular approach and improves on the worst case iteration bound of the classical algorithm.

Keywords

linear optimizationinterior point methodsself-regular functionspolynomial complexity

MSC classification

Secondary: 90C05: Linear programming
Type
Research Article
Information
The ANZIAM Journal , Volume 51 , Issue 2 , October 2009 , pp. 286 - 301
Copyright
Copyright © Australian Mathematical Society 2010

References

[1]Andersen, E. D. and Andersen, K. D., “The MOSEK interior point optimizer for linear programming: an implementation of the homogeneous algorithm”, in: High performance optimization, (eds Frenk, H., Roos, K., Terlaky, T. and Zhang, S.), (Kluwer Academic Publishers, Dordrecht, 2000) 197–232.Google Scholar
[2] CPLEX: ILOG optimization. http://www.ilog.com.Google Scholar
[3]Karmarkar, N. K., “A new polynomial-time algorithm for linear programming”, Combinatorica 4 (1984) 373–395.Google Scholar
[4]Megiddo, N., “Pathways to the optimal set in linear programming”, in: Progress in mathematical programming: interior point and related methods, (ed. Megiddo, N.), (Springer, New York, 1989) 131–158. (Identical version in: Proc. 6th Mathematical Programming Symp. of Japan, Nagoya, Japan, 1986, 1–35.)Google Scholar
[5]Mehrotra, S., “On the implementation of a (primal-dual) interior point method”, SIAM J. Optim. 2 (1992) 575–601.CrossRefGoogle Scholar
[6]Peng, J., Roos, C. and Terlaky, T., Self-regularity: a new paradigm for primal-dual interior-point methods (Princeton University Press, Princeton, NJ, 2002).Google Scholar
[7]Roos, C., Terlaky, T. and Vial, J.-Ph., Interior point algorithms for linear optimization, 2nd edn (Springer, New York, 2006).Google Scholar
[8]Salahi, M., “New adaptive interior point algorithms for linear optimization”, Ph. D. Thesis, Department of Mathematics and Statistics, McMaster University, 2006.Google Scholar
[9]Sonnevend, G., “An ‘analytic center’ for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming”, in: System modeling and optimization: proceedings of the 12th IFIP conference, Budapest, Hungary, September 1985, Volume 84 of Lecture Notes in Control and Information Sciences (eds A. Prékopa, J. Szelezsán and B. Strazicky), (Springer, Berlin, 1986) 866–876.Google Scholar
[10]Wright, S. J., Primal-dual interior-point methods (SIAM, Philadelphia, PA, 1997).Google Scholar
[11]Ye, Y., Interior point algorithms, theory and analysis (Wiley, Chichester, 1997).Google Scholar
[12]Zhang, Y., “Solving large-scale linear programs by interior point methods under the MATLAB environment”, Optim. Methods Softw. 10 (1999) 1–31.CrossRefGoogle Scholar