GAMS — The Solver Manuals - Available Software

CONOPT 147
The necessary information is related to the order of the variables and equations and number of occurrences of
variables and equations, and since GAMS does no have a natural place for this type of information CONOPT
returns it in the marginals of the equations and variables. The solution order for the triangular equations and
variables that have been solved successfully are defined with positive numbers in the marginals of the equations
and variables. For the remaining non- triangular variables and equations CONOPT shows the number of places
they appear as negative numbers, i.e. a negative marginal for an equation shows how many of the non- triangular
variables that appear in this equation. You must fix one or more variables until at least one of the non-triangular
equation only has one non-fixed variable left.
2. Infeasibilities due to bounds: If some of the triangular equations cannot be solved with respect to their
variable because the variable will exceed the bounds, then CONOPT will flag the equation as infeasible, keep
the variable at the bound, and continue the triangular solve. The solution to the triangular model will therefore
satisfy all bounds and almost all equations. The termination message will be
** Infeasible solution. xx artificial(s) have been
introduced into the recursive equations.
and the model status will be 5, Locally Infeasible.
The modeler may in this case add explicit artificial variables with high costs to the infeasible constraints and
the resulting point will be an initial feasible point to the overall optimization model. You will often from the
mathematics of the model know that only some of the constraints can be infeasible, so you will only need to check
whether to add artificials in these equations. Assume that a block of equations MATBAL(M,T) could become
infeasible. Then the artificials that may be needed in this equation can be modeled and identified automatically
with the following GAMS constructs:
SET APOSART(M,T) Add a positive artificial in Matbal
ANEGART(M,T) Add a negative artificial in Matbal;
APOSART(M,T) = NO; ANEGART(M,T) = NO;
POSITIVE VARIABLE
VPOSART(M,T) Positive artificial variable in Matbal
VNEGART(M,T) Negative artificial variable in Matbal;
MATBAL(M,T).. Left hand side =E= right hand side
+ VPOSART(M,T)$APOSART(M,T) - VNEGART(M,T)$ANEGART(M,T);
OBJDEF.. OBJ =E= other_terms +
WEIGHT * SUM((M,T), VPOSART(M,T)$APOSART(M,T)
+VNEGART(M,T)$ANEGART(M,T) );
Solve triangular model ...
APOSART(M,T)$(MATBAL.L(M,T) GT MATBAL.UP(M,T)) = YES;
ANEGART(M,T)$(MATBAL.L(M,T) LT MATBAL.LO(M,T)) = YES;
Solve final model ...
3. Small pivots: The triangular facility requires the solution of each equation to be locally unique which also
means that the pivots used to solve each equation must be nonzero. The model segment
E1 .. X1 =E= 0;
E2 .. X1 * X2 =E= 0;
will give the message