dc.contributor.author Liao, A. en_US dc.date.accessioned 2007-04-04T13:07:23Z dc.date.available 2007-04-04T13:07:23Z dc.date.issued 1994-08 en_US dc.identifier.citation http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.tc/94-191 en_US dc.identifier.uri https://hdl.handle.net/1813/5526 dc.description.abstract In the paper of Liao and Todd [3] two weighted centers are introduced and used to design algorithms for solving systems of linear inequalities. The linear programming problems can be solved via the weighted centers of a sequence of linear inequalities formed by letting the objective be an extra constraint and increasing the lower bound corresponding to the objective function as long as it is possible. In this paper we study the second kind of weighted center of [3] which ismore computationally oriented and show that, under a regularity assumption, the weighted center of the linear inequality with the objective as an extra constraint converges to the solution of the linear programming problem under consideration as the upper bound corresponding to the objective function is pulled towards the infinity. We propose a relaxed version of one of the algorithms of [3]. This modified version does not try to find an accurate center during each iteration; instead, an approximate center which is the k-th feasible iterate is determined in the k-th iteration. We show that this modified algorithm finds an e-solution in finity many iterations. Some limited numerical results are presented to compare our algorithm with the simplex method and indicate that our algorithm is promising. en_US dc.format.extent 186591 bytes dc.format.extent 233112 bytes dc.format.mimetype application/pdf dc.format.mimetype application/postscript dc.language.iso en_US en_US dc.publisher Cornell University en_US dc.subject theory center en_US dc.subject weighted center en_US dc.subject Newton's method en_US dc.subject linear programming en_US dc.title Pull the Weighted Center Towards the Solution of LP en_US dc.type technical report en_US
﻿