Linear Complementarity and Oriented Matroids

Linear Complementarity and Oriented Matroids (1990)

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by Komei Fukuda , Tamas Terlaky

Venue:	Journal of the Operational Research Society of Japan
Citations:	12 - 8 self

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Datum	Value	Source
TITLE	Linear Complementarity and Oriented Matroids	user correction - Legacy Corrections
AUTHOR NAME	Komei Fukuda	SVM HeaderParse 0.1
AUTHOR AFFIL	University of Tsukuba	SVM HeaderParse 0.2
AUTHOR ADDR	3-29-1 Otsuka, Bunkyo-ku; Tokyo 112, Japan	SVM HeaderParse 0.1
AUTHOR NAME	Tamas Terlaky	SVM HeaderParse 0.1
AUTHOR AFFIL	y; Faculty of Technical Mathematics and Informatics; Delft University of Technology	SVM HeaderParse 0.2
AUTHOR ADDR	P.O. Box 35, 2600 AJ Delft; Netherlands	SVM HeaderParse 0.1
ABSTRACT	A combinatorial abstraction of the linear complementarity theory in the setting of oriented matroids was rst considered by M.J. Todd. In this paper, we take a fresh look at this abstraction, and attempt to give a simple treatment of the combinatorial theory of linear complementarity. We obtain new theorems, proofs and algorithms in oriented matroids whose specializations to the linear case are also new. For this, the notion of suciency of square matrices, introduced by Cottle, Pang and Venkateswaran, is extended to oriented matroids. Then, we prove a sort of duality theorem for oriented matroids, which roughly states: exactly one of the primal and the dual system has a complementary solution if the associated oriented matroid satisfies "weak" sufficiency. We give two different proofs for this theorem, an elementary inductive proof and an algorithmic proof using the criss-cross method which solves one of the primal or dual problem by using surprisingly simple pivot rules (without any pertur...	user correction - Legacy Corrections
YEAR	1990	user correction - Legacy Corrections
VENUE	Journal of the Operational Research Society of Japan	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	45--61	INFERENCE
VOLUME	35	INFERENCE
CITATIONS	25 found	ParsCit 1.0