Interior point approach to linear programming: theory, algorithms & parametric analysis

1992 ◽  
pp. 181-216 ◽  
Author(s):  
C. Roos
Keyword(s):  
Linear Programming ◽  
Interior Point ◽  
Parametric Analysis ◽  
Programming Theory

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 new efficient short-step projective interior point method for linear programming

2018 ◽  
Vol 46 (3) ◽  
pp. 291-294
Author(s):  
Mousaab Bouafia ◽  
Djamel Benterki ◽  
Adnan Yassine
Keyword(s):  
Linear Programming ◽  
Interior Point ◽  
Interior Point Method ◽  
Point Method
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