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Tolerance in LinearProgramming

  • To: mathgroup at smc.vnet.net
  • Subject: [mg98768] Tolerance in LinearProgramming
  • From: Slava Rychkov <rychkov at sns.it>
  • Date: Sat, 18 Apr 2009 03:39:25 -0400 (EDT)

Hi!

I would like to understand better the meaning of the Tolerance parameter
in LinearProgramming. For example, I would like to understand why

M = {{1000.,
     300., -300.0}, {10., -2000., -1.}, {100000., -1000., -90.}};
LinearProgramming[{0, 0, 0}, M, {0, 0, 0}, {1, 1, 1},
  Tolerance -> 0.1]

does not find a solution, while with smaller Tolerance it does:

LinearProgramming[{0, 0, 0}, M, {0, 0, 0}, {1, 1, 1},
  Tolerance -> 0.01]

Naively, I find this behavior counterintuitive.
Thanks a lot,

-- 
Vyacheslav Rychkov                https://mail.sns.it/~rychkov
Scuola Normale Superiore          Tel: +39-050-509068 (office)
Classe di Scienze                      +39-050-3820086  (home)
Piazza dei Cavalieri, 7                +39-3403925168 (mobile)
56100 Pisa                        Fax: +39-050-509045
Italy                             E-mail: Rychkov at sns.it


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