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Dikin's algorithm for matrix linear programming problems

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System Modelling and Optimization

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 197))

Abstract

We construct a generalization of affine-scaling vector fields for matrix linear programming problems. We discuss various properties of these vector fields and suggest a generalization of Dikin's algorithm.

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References

  1. E.R. Barnes, A variation on Karmarkar's algorithm for solving linear programming problems, Math. Programming, 36(1986), 174–182.

    Article  MATH  MathSciNet  Google Scholar 

  2. D.A. Bayer and J.C. Lagarias, The nonlinear geometry of linear programming.I, Trans. Amer. Math. Soc., 314(1989), 499–526.

    MATH  MathSciNet  Google Scholar 

  3. I. Dikin, Iterative solution of problems of linear and quadratic programming, Soviet. Math. Dokl., 8(1967),674–675.

    MATH  Google Scholar 

  4. L. Faybusovich, Hamiltonian structure of dynamical systems which solve linear programming problems, Physica D53(1991), 217–232.

    MathSciNet  Google Scholar 

  5. R. Fletcher, Semi-definite constraints in optimization, SIAM J. Control Optim., 23(1985),493–513.

    Article  MATH  MathSciNet  Google Scholar 

  6. Yu.E. Nesterov and A.S. Nemirovsky, Self-concordant functions and polynomial time methods in convex programming. Technical report, Centr. Econ. and Math. Inst., Moscow,USSR, 1989.

    Google Scholar 

  7. G. Sonnevend, Applications of analytic centers. In: Numerical Linear algebra, Digital Signal Processing and Parallel Algorithms, Springer, 1991.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Notre Dame Mail distribution Center, 46556-5683, Notre Dame, IN

    Leonid Faybusovich

Authors
  1. Leonid Faybusovich
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Jacques Henry Jean-Pierre Yvon

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© 1994 Springer-Verlag

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Faybusovich, L. (1994). Dikin's algorithm for matrix linear programming problems. In: Henry, J., Yvon, JP. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 197. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035472

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  • DOI: https://doi.org/10.1007/BFb0035472

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19893-2

  • Online ISBN: 978-3-540-39337-5

  • eBook Packages: Springer Book Archive

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