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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 58, 2009 - Issue 8
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Original Articles

Sign consistent linear programming problems

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Pages 935-946 | Received 08 Nov 2006, Accepted 11 Jun 2007, Published online: 02 Nov 2009

References

  • Ando , T . 1987 . Totally positive matrices . Linear Algebra Appl. , 90 : 165 – 219 .
  • Bartels , RH . 1971 . A stabilization of the simplex method . Numer. Math. , 16 : 414 – 434 .
  • Brown , LD , Johnstone , IM and MacGibbon , KB . 1981 . Variation diminishing transformations: a direct approach to total positivity and its statistical applications . J. Am. Stat. Assoc. , 76 : 824 – 832 .
  • Carnicer , JM , García-Esnaola , M and Peña , JM . 1996 . Generalized convexity preserving transformations . Comp. Aid. Geomet. Des. , 13 : 179 – 197 .
  • Cheung , D and Cucker , F . 2001 . A new condition number for linear programming . Math. Program. , 91 : 163 – 174 .
  • Cheung , D and Cucker , F . 2004 . Solving linear programs with finite precision: I. condition numbers and random programs . Math. Program. , 99 : 175 – 196 .
  • Cucker , F and Wschebor , M . 2003 . On the expected condition number of linear programming problems . Numer. Math. , 94 : 419 – 478 .
  • Darracq-Calmettes , MC and Dedieu , J-P . 2002 . Backward error analysis for the linear programming problem . Optimization , 51 : 1 – 10 .
  • Epelman , M and Freund , RM . 2002 . A new condition measure, preconditioners, and relations between different measures of conditioning for conic linear systems . SIAM J. Optim. , 12 : 627 – 655 .
  • Gasca , M and Micchelli , CA . 1996 . Total Positivity and its Applications , Dordrect : Kluwer Academic Publishers .
  • Higham , NJ . 2002 . Accuracy and Stability of Numerical Algorithms , 2ndedition , 165 – 172 . Philadelphia : SIAM .
  • Karlin , S . 1968 . Total Positivity , Stanford : Stanford University Press .
  • Murty , KG . 1983 . Linear Programming , New York : John Wiley & Sons .
  • Ordóñez , F and Freund , RM . 2003 . Computational experience and the explanatory value of condition measures for linear optimization . SIAM J. Optim. , 14 : 307 – 333 .
  • Peña , JM . 1995 . Matrices with sign consistency of a given order . SIAM J. Matrix Anal. Appl. , 16 : 1100 – 1106 .
  • Peña , JM . 1997 . Backward stability of a pivoting strategy for sign-regular linear systems . BIT , 37 : 910 – 924 .
  • Peña , JM . 1999 . Shape Preserving Representations in Computer-Aided Geometric Design , Commack : Nova Science Publishers, Inc. .
  • Prékopa , A . 1990 . “ Totally positive linear programming problem ” . In in Functional Analysis, Optimization, and Mathematical Economics , New York : Oxford University Press .
  • Renegar , J . 1996 . Condition numbers, the barrier method and the conjugate-gradient method . SIAM J. Optim. , 6 : 879 – 912 .

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