Skip to main content


eCommons@Cornell

eCommons@Cornell >
College of Engineering >
Computer Science >
Computer Science Technical Reports >

Please use this identifier to cite or link to this item: http://hdl.handle.net/1813/6169
Title: An Accelerated Interior Point Method Whose Running Time Depends Only on $A$
Authors: Vavasis, Stephen A.
Ye, Yinyu
Keywords: computer science
technical report
Issue Date: Oct-1993
Publisher: Cornell University
Citation: http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR93-1391
Abstract: We propose a "layered-step" interior point (LIP) algorithm for linear programming. This algorithm follows the central path, either with short steps or with a new type of step called a "layered least squares" (LLS) step. The algorithm returns the exact global minimum after a finite number of steps-in particular, after $O(n^{3.5}c(A))$ iterations, where $c(A)$ is a function of the coefficient matrix. The LLS steps can be thought of as accelerating a path-following interior point method whenever near-degeneracies occur. One consequence of the new method is a new characterization of the central path: we show that it composed of at most $n^2$ alternating straight and curved segments. If the LIP algorithm is applied to integer data, we get as another corollary a new proof of a well-known theorem by Tardos that linear programming can be solved in strongly polynomial time provided that $A$ contains small-integer entries.
URI: http://hdl.handle.net/1813/6169
Appears in Collections:Computer Science Technical Reports

Files in This Item:

File Description SizeFormat
93-1391.pdf4.47 MBAdobe PDFView/Open
93-1391.ps844.95 kBPostscriptView/Open

Refworks Export

Items in eCommons are protected by copyright, with all rights reserved, unless otherwise indicated.

 

© 2014 Cornell University Library Contact Us