Rank-one techniques in log-barrier function methods for linear programming

1994 ◽  
Vol 82 (2) ◽  
pp. 405-413 ◽  
Author(s):  
S. Q. Wu ◽  
F. Wu
Keyword(s):  
Linear Programming ◽  
Barrier Function ◽  
Rank One

NEWTON FLOW AND INTERIOR POINT METHODS IN LINEAR PROGRAMMING

2005 ◽  
Vol 15 (03) ◽  
pp. 827-839 ◽  
Author(s):  
JEAN-PIERRE DEDIEU ◽  
MIKE SHUB
Keyword(s):  
Linear Programming ◽  
Vector Field ◽  
Interior Point ◽  
Barrier Function ◽  
Interior Point Methods ◽  
Logarithmic Barrier Function ◽  
Programming Theory ◽  
Central Paths ◽  
Logarithmic Barrier

We study the geometry of the central paths of linear programming theory. These paths are the solution curves of the Newton vector field of the logarithmic barrier function. This vector field extends to the boundary of the polytope and we study the main properties of this extension: continuity, analyticity, singularities.

A multiplicative barrier function method for linear programming

Algorithmica ◽  
1986 ◽  
Vol 1 (1-4) ◽  
pp. 455-482 ◽  
Author(s):  
Masao Iri ◽  
Hiroshi Imai
Keyword(s):  
Linear Programming ◽  
Barrier Function ◽  
Function Method
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