Journal article
The Worst-Case Step in Karmarkar's Algorithm
Mathematics of operations research, Vol.14(2), pp.294-302
05/01/1989
DOI: 10.1287/moor.14.2.294
Abstract
In this note we consider the worst-case performance in a single step of Karmarkar's projective algorithm for linear programming. In the transformed problem which arises on each iteration we show that the critical ratio “r/R” can be improved (asymptotically) by a factor of two. We also show that in the original problem, where performance is characterized by reduction in the potential function, the worst-case reduction can be improved to approximately 0.72. Moreover, we demonstrate that both of these bounds are tight, so that no further improvement based on the analysis of a single step is possible.
Details
- Title: Subtitle
- The Worst-Case Step in Karmarkar's Algorithm
- Creators
- Kurt M. Anstreicher - Yale School of Organization and Management, Box 1A, New Haven, Connecticut 06520
- Resource Type
- Journal article
- Publication Details
- Mathematics of operations research, Vol.14(2), pp.294-302
- DOI
- 10.1287/moor.14.2.294
- ISSN
- 0364-765X
- eISSN
- 1526-5471
- Language
- English
- Date published
- 05/01/1989
- Academic Unit
- Industrial and Systems Engineering; Computer Science; Business Analytics
- Record Identifier
- 9984380417202771
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