Optimization Online


A New and Efficient Large-Update Interior-Point Method for Linear Optimization

J Peng (pengj***at***cas.mcmaster.ca)
C Roos (C.Roos***at***its.tudelft.nl)
T Terlaky (terlaky***at***pop.cas.mcmaster.ca )

Abstract: Recently, the authors presented a new large-update primal-dual method for Linear Optimization, whose $O(n^\frac23\,\log\frac{n}{\e})$ iteration bound substantially improved the classical bound for such methods, which is $O\br{n\log\frac{n}{\e}}$. In this paper we present an improved analysis of the new method. The analysis uses some new mathematical tools developed before when we considered a whole family of interior-point methods which contains the method considered in this paper. The new analysis yields an $O\br{\sqrt{n}\log n\,\log\frac{n}{\e}}$ iteration bound for large-update methods. Since we concentrate on one specific member of the family mentioned before, the analysis significantly simplifies. The new bound further improves the iteration bound for large-update methods, and is quite close to the currently best iteration bound known for interior-point methods, namely $O\br{\sqrt{n}\,\log\frac{n}{\e}}$. Hence, the existing gap between the iteration bounds for small-update and large-update methods is substantially narrowed.

Keywords: Linear optimization, interior-point method, primal-dual Newton method, large-update method, polynomial complexity

Category 1: Linear, Cone and Semidefinite Programming

Citation: TU Delft, NL/McMaster University, Hamilton January 2001

Download: [Postscript][PDF]

Entry Submitted: 01/31/2001
Entry Accepted: 01/31/2001
Entry Last Modified: 01/31/2001

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Programming Society