>> What I am trying to obtain is that though using LPR, the solution >> is bounded, but the solution does not satisfy what I need which is >> "x1+x2<=1" which means that "x1" and "x2" cannot co-exist together in >> a solution. > > In mathematics "x1+x2<=1" does not mean "that x1 and x2 cannot co-exist > together in a solution"; it means that the sum of x1 and x2 is not > greater than 1. The constraint you need is "NOT x1 OR NOT x2"; this > constraint is *not* equivalent to "x1+x2<=1" until x1 and x2 are > restricted to be binary, and being non-convex this constraint cannot be > modeled within linear program (LP). If you restrict some variables to > be binary, you get integer program (MIP), not LP.
I would like to add that there exists a version of the simplex method (which is not implemented in glpk), where you can declare a set of variables {x1, x2, ..., xk} to be so called Special Ordered Set of Type 1 (SOS1 for brevity). SOS1 means that at most one of its variables can be basic while all its other variables must be non-basic. Assuming that all variables are non-negative, i.e. xj >= 0, SOS1 then means that at most one of its variables can take non-zero value while values of its other variables must be zero. Processing SOS1 constraints can be easily embedded into the simplex method: if some SOS1 variable is basic, a non-basic variable from the same SOS1 must not be chosen to enter the basis. However, in general case such version of the simplex method can find only a local optimum, because SOS1 constraints are non-convex. _______________________________________________ Help-glpk mailing list Help-glpk@gnu.org http://lists.gnu.org/mailman/listinfo/help-glpk