GAMS/PATH User Guide Version 4.3

variables x;
equations d_f;
x.lo = 0;
x.up = 2;
d_f.. 2*(x - 1) =e= 0;
model first / d_f.x /;
solve first using mcp;
Figure 1.5: First order conditions as an MCP, first.gms
are derived from the bounds on the associated variable. Before solving the
problem, for finite bounded variables, we do not know if the associated function
will be positive, negative or zero at the solution. Thus, we do not know
whether to define the equation as “=e=”, “=l=” or “=g=”. GAMS therefore
allows any of these, and informs the modeler via the “REDEF” label that
internally GAMS has redefined the bounds so that the solver processes the
correct problem, but that the solution given by the solver does not satisfy
the original bounds. However, in practice, a REDEF can also occur when the
equation is defined using “=e=” and the variable has a single finite bound.
This is allowed by GAMS, and as above, at a solution of the complementarity
problem, the variable is at its bound and the function F does not satisfy the
“=e=” relationship.
Note that this is not an error, just a warning. The solver has solved the
complementarity problem specified by this equation. GAMS gives this report
to ensure that the modeler understands that the complementarity problem
derives the relationships on the equations from the bounds, not from the
equation definition.
1.4 Pitfalls
As indicated above, the ordering of an equation is important in the specification
of an MCP. Since the data of the MCP is the function F and the bounds
ℓ and u, it is important for the modeler to pass the solver the function F and
not −F .
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