Solving linear system of equalities AND disequalities

Hi all,

Given I have a linear system of m constraints in m variables of
equalities and disequalities what's the best way to handle the
existence of disequalities? Is there any known algorithm that handles
this? I'm currently using OMEGA Test and Fourier-Motzkin Variable
elimination for inequalities (real and integer constraints).
To handle the equalities I would do equality elimination and substitute
the corresponding variables in the inequalities system. However I still
have the disequalities which I do not have an idea on how to handle
them. The first thing it comes to my mind it to get a solution from the
rest of the system and check if it is accepted by the inequalities. If
it is the solution is OK, otherwise we need other solution. If there
are no more solutions, the whole system has no solution.

Any ideas? Comments?

Cheers,

Paulo Matos

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