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Isospectral flows and linear programming

Published online by Cambridge University Press:  17 February 2009

U. Helmke
U. Helmke
Affiliation:
University of Regensburg, Department of Mathematics, 8400 Regensburg, Germany.
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Abstract

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Brockett 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.

Type
Research Article
Information
The ANZIAM Journal , Volume 34 , Issue 4 , April 1993 , pp. 495 - 510
Copyright
Copyright © Australian Mathematical Society 1993

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