Chapter 3 Large sparse linear programming

Part of the Lecture Notes in Computer Science book series (LNCS, volume 165)


Linear Programming Problem Simplex Method Cholesky Factor Strong Component Secondary Storage 
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3.14 References

  1. Bartels R., and Golub G. [1969]. The simplex method of linear programming using LU decomposition, Comm. ACM 12, 266–268.Google Scholar
  2. Bartels, R. [1971]. A stabilization of the simplex method, Numer. Math. 16, 414–434.Google Scholar
  3. Bartels, R. [1976]. Large Sparse Linear Programming, Applied Matrix Methods Workshop, Johns Hopkins University, Baltimore, Maryland.Google Scholar
  4. Dantzig, G. [1963]. Linear Programming and Extensions, Princeton University Press, Princeton, New Jersey.Google Scholar
  5. Forrest J. and Tomlin [1972]. Updating the triangular factors of the basis to maintain sparsity in the product form simplex method, Mathematical Programming 2, 263–278.Google Scholar
  6. Gill, P., and Murray, W., [1973]. A numerically stable form of the simplex algorithm, Algebra and Its Applics. 7, 99–138.Google Scholar
  7. Gill, P., Murray, W., and Wright, M. [1981]. Practical Optimization, Academic Press, New York.Google Scholar
  8. Gay, D.M [1979]. On combining the schemes of Reid and Saunders for sparse LP bases, in Sparse Matrix Proceedings 1978, Duff and Stewart (eds), SIAM, Philadelphia.Google Scholar
  9. Goldfarb, D. [1976]. Using the steepest-edge simplex algorithm to solve sparse linear programs, in Sparse Matrix Computations, Bunch and Rose (eds), Academic Press, New York.Google Scholar
  10. Hellerman, E., and Rarick, D. [1972]. The partitioned pre-assigned pivot procedure, in Sparse Matrices and Their Applications, Rose and Willoughby (eds), Plenum Press, New York.Google Scholar
  11. Orchard-Hays, W. [1968]. Advanced Linear-Programming Computing Techniques, McGraw-Hill, New YorkGoogle Scholar
  12. Reid, J. K. [1982]. A sparsity-exploiting variant of the Bartels-Golub decomposition for linear programming bases, Mathematical Programming 24, 55–69.Google Scholar
  13. Saunders, M [1972]. Large-scale linear programming using the Cholesky factorization, PhD Dissertation, Stanford University, Stanford CA.Google Scholar
  14. Saunders, M. [1976]. A fast, stable implementation of the simplex method using Bartels-Golub updating, in Sparse Matrix Computations, Bunch and Rose, eds.,Academic Press, New York.Google Scholar
  15. Tarjan, R. [1972]. Depth first search and linear graph algorithms, SIAM J. Computing 1, 146–160.Google Scholar

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© Springer-Verlag Berlin Heidelberg 1984

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