[Coin-standards] Re: Sparse matrix representation

[Leonardo B. Lopes]

On Wed, 17 Apr 2002, Gus Gassmann wrote:

> I disagree. How can you model chance constraints if not by giving 
> distribution information? So I don't think it matters whether we are 
> talking about SMPS or the big picture. And with the sampling 
> approaches of Infanger and Higle and Sen, the discretization is part 
> of the algorithm, making the continuous distributions part of the 
> instance. It would be a mistake to ignore those problems.

You're right. It doesn't matter if we're talking about SMPS or the big
picture, and you defninetely need distributions for modeling chance
constraints. My logic for having the distributions in the nonlinear part
is that Higle and Sen or Infanger are actually solving a nonlinear problem
by doing some clever sampling and solving some linear programs as
subproblems, while MSLiP is actually solving a really really large linear
program with special structure. Plus, isolating the distribution
information from the linear programming part makes it simpler for the
solvers that are already out there to build parsers.

The alternative would be to represent that constraint by flagging (or not)
an element of the linear part as randomly distributed, and providing a
distribution at some other point (like SMPS), or including the
distribution info there (which is possible), which would make those
expressions nonlinear anyway...

> > Actually, I think there might be a relatively elegant way of
> > communicating chance constraints. In SNOML there are <rowset> tags
> > with probability parameters, which default to 1.
> 
> That's a start, but I don't see (off-hand) how you can model multi-
> dimensional chance-constraints in this fashion. 
> 

Chance constraints, whether single or multidimensional, are handled in
snoml (as of now) by specifying the "prob" attribute of a <rowset>. So if
the <rowset> includes more than one row, all those rows are taken together
to have probability p. If they are linear, or nonlinear, it doesn't really
change the syntax either.

Cheers,
Leo.

========================================================================
Leonardo B. Lopes                                       leo at iems.nwu.edu 
Ph.D. Student                                              (847)491-8470
IEMS - Northwestern University              http://www.iems.nwu.edu/~leo