On Thursday, August 30, 2012 4:50:24 PM UTC+2, Gordon Sande wrote:
> On 2012-08-30 10:58:52 -0300, A.L. said:
> > On Wed, 29 Aug 2012 23:09:33 -0700 (PDT), SonTA
> > <taanhson...@gmail.com> wrote:
> >> On Thursday, August 30, 2012 1:36:38 AM UTC+2, Paul wrote:
> >>> Short answer: Change the objective function.
> >>> Slightly longer answer: This is a (somewhat) Frequently Asked Question.
> >>> Search the group for previous answers about enumerating vertices. (As
> >>> A. L. suggests, you can also use Google, which will turn up links to
> >>> several journal articles on the subject.)
> >>> A. L.: Good to see you're still around!
> >> Many thanks!
> > Look for Chernikova algorithm
> > http://www.mathnet.ru/links/d7d0006729a5900ca4c6f22757f5f2de/zvmmf720...
> > Unfortunately, teh above link leads to artiucle in Russian :) However,
> > there is enough information about this algorithm in English. Use
> > google
> > A.L.
> Try the work of either David Avis or Komei Fukuda. They both
> collaborate and do their own things.
> Davis has a reverse search algorithm called lrs now at version 4.2. He
> is at McGill.
> Fukuda has an enumeration package called cdd based on the double
> description method. There
> seem to be several versions. He is at ETH Zurich.
> Chernikova, cdd, etc are all descendents of Fourier elimination. They
> vary in how they
> do the bookkeeping and avoid redundency.
In fact, my problem come from solving a Mix 0-1 linear programming by combined with a cutting plane method, but in worst case, the valid inequality which uses to generate the cutting plane is identical with a face of the polyhedron (the worst problem is that I don't know if there exists a 0-1 feasible vertex in this face of polyhedron or not?) and I try to escape form this point.
