Linear Programming: Karmarkar Projective Algorithm, Karmarkar Algorithm

2012 ◽  
Keyword(s):  
Linear Programming ◽  
Projective Algorithm ◽  
Karmarkar Algorithm

scholarly journals A variable-metric variant of the Karmarkar algorithm for linear programming

1987 ◽  
Vol 39 (1) ◽  
pp. 1-20 ◽  
Author(s):  
J. E. Dennis ◽  
A. M. Morshedi ◽  
Kathryn Turner
Keyword(s):  
Linear Programming ◽  
Variable Metric ◽  
Karmarkar 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 Centered Projective Algorithm for Linear Programming

1990 ◽  
Vol 15 (3) ◽  
pp. 508-529 ◽  
Author(s):  
Michael J. Todd ◽  
Yinyu Ye
Keyword(s):  
Linear Programming ◽  
Projective Algorithm
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