karmarkar algorithm
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2017 ◽  
Vol 72 ◽  
pp. 205-217
Author(s):  
Hui Zhu ◽  
Hongwei Liu ◽  
Carol XJ Ou ◽  
Robert M. Davison ◽  
Zherui Yang

Author(s):  
U. Helmke

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.


1991 ◽  
Vol 25 (2) ◽  
pp. 209-235
Author(s):  
Abdellah Salhi ◽  
George R. Lindfield
Keyword(s):  

1987 ◽  
Vol 39 (1) ◽  
pp. 1-20 ◽  
Author(s):  
J. E. Dennis ◽  
A. M. Morshedi ◽  
Kathryn Turner

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