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Condition numbers for linear program...

Cornell University.

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Condition numbers for linear programming.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Condition numbers for linear programming./
Author:	Pena, Javier Francisco.
Description:	134 p.
Notes:	Adviser: James Renegar.
Contained By:	Dissertation Abstracts International59-06B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9837858
ISBN:	9780591915068

Condition numbers for linear programming.
Pena, Javier Francisco.

Condition numbers for linear programming. - 134 p.

Adviser: James Renegar.

Thesis (Ph.D.)--Cornell University, 1998.

For a feasible conic system of constraints$$\eqalign{Ax&=b\cr x&\ge0,\cr}$

ISBN: 9780591915068Subjects--Topical Terms:

515831
Mathematics.

Condition numbers for linear programming.
LDR:02532nam 2200325 a 45 001 859508
005 20100713
008 100713s1998 ||||||||||||||||| ||eng d
020 $a 9780591915068
035 $a (UMI)AAI9837858
035 $a AAI9837858
040 $a UMI $c UMI
100 1 $a Pena, Javier Francisco. $3 1026707
245 1 0 $a Condition numbers for linear programming.
300 $a 134 p.
500 $a Adviser: James Renegar.
500 $a Source: Dissertation Abstracts International, Volume: 59-06, Section: B, page: 2793.
502 $a Thesis (Ph.D.)--Cornell University, 1998.
520 $a For a feasible conic system of constraints$$\eqalign{Ax&=b\cr x&\ge0,\cr}$ $t he condition number is defined in terms of the data perturbations which yield infeasible systems, that is, in terms of "infeasible perturbations."
520 $a This work conveys various results regarding condition numbers for linear programming. Like traditional condition numbers for linear equations, these numbers aim to capture how changes in the data of the linear program affect properties of the solutions.
520 $a This thesis addresses three main themes. First, we study some geometric properties of the set of infeasible perturbations of a conic system. It is shown how the geometry of infeasible perturbations for linear equations extends naturally to conic systems.
520 $a Second, we propose a way to solve the problem of finding a solution for a conic system of constraints by reformulating the problem as an optimization problem to be solved via interior-point methods (IPMs). The approach provides both backward and forward-approximate solutions for a given conic system. The behavior of the IPM bears a close connection with the condition number of the conic system; in particular, the condition numbers of the linear systems that need to be solved when applying the IPM are always bounded in terms of the condition number of the conic system.
520 $a Third, we combine some key results established in Chapters 2 and 3 to design several schemes to effectively estimate the condition number of a conic system. In addition to theoretical guarantees on the quality of the estimates, we perform numerical experiments to illustrate the behavior of the proposed schemes in practice.
590 $a School code: 0058.
650 4 $a Mathematics. $3 515831
650 4 $a Operations Research. $3 626629
690 $a 0405
690 $a 0796
710 2 $a Cornell University. $3 530586
773 0 $t Dissertation Abstracts International $g 59-06B.
790 $a 0058
790 1 0 $a Renegar, James, $e advisor
791 $a Ph.D.
792 $a 1998
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9837858