A parallel interior point algorithm for linear programming on a network of transputers

1993 ◽  
Vol 43 (2) ◽  
pp. 49-86 ◽  
Author(s):  
R. H. Bisseling ◽  
T. M. Doup ◽  
L. D. J. C. Loyens
Keyword(s):  
Linear Programming ◽  
Interior Point ◽  
Interior Point Algorithm

Isospectral flows and linear programming

1993 ◽  
Vol 34 (4) ◽  
pp. 495-510
Author(s):  
U. Helmke
Keyword(s):  
Linear Programming ◽  
Interior Point ◽  
Continuous Time ◽  
Compact Convex ◽  
Optimal Solution ◽  
Symmetric Matrices ◽  
Interior Point Algorithm ◽  
Convex Constraints ◽  
Linear Programming Problems ◽  
Karmarkar Algorithm

AbstractBrockett has studied the isospectral flow Ḣ = [H, [H, N]], with [A, B] = AB ∔ BA, on spaces of real symmetric matrices. The flow diagonalises real symmetric matrices and can be used to solve linear programming problems with compact convex constraints. We show that the flow converges exponentially fast to the optimal solution of the programming problem and we give explicit estimates for the time needed by the flow to approach an ε-neighbourhood of the optimum. An interior point algorithm for the standard simplex is analysed in detail and a comparison is made with a continuous time version of Karmarkar algorithm.

scholarly journals A modified layered-step interior-point algorithm for linear programming

1998 ◽  
Vol 82 (3) ◽  
pp. 339-355 ◽  
Author(s):  
Nimrod Megiddo ◽  
Shinji Mizuno ◽  
Takashi Tsuchiya
Keyword(s):  
Linear Programming ◽  
Interior Point ◽  
Interior Point Algorithm
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