Re: [Help-glpk] Solving linear/nonlinear systems of equations via glpk

[Andrew Makhorin]

> In an academic paper it is claimed finding all solutions to non linear
> systems of equations by using glpk.There, dual simplex method is said
> to use. 
> My question is how we can define this problem in glpk to have the
> solutions.
> In other words how can we define a problem about solving systems of
> linear/nonlinear equations using glpk?
> Can you please give some examples about this?

There exists a known technique to find all solutions of a system of
nonlinear equations by using a version of the branch-and-bound search,
where the domain is divided into boxes, and interval arithmetic is used
to prove that a box contains no solution. The main idea to strengthen
the check is to use a polyhedral description rather than interval
arithmetic. See, for example, the following paper I googled:
http://www.ieice.org/proceedings/NOLTA2007/articles/18AM2-E-2-Suda.pdf

AFAIK, a similar approach (i.e. based on polyhedral descruption) is used
to optimize the code produced by a compiler; see, for example,
http://gcc.gnu.org/wiki/Graphite .