GAMS — The Solver Manuals - Available Software

CONOPT 133
The remaining two sections give some short guidelines for selecting non-default options (section A12), and
discuss miscellaneous topics (section A13) such as CONOPT’s facilities for strictly triangular models (A13.1) and
for square systems of equations, in GAMS represented by the model class called CNS or Constrained Nonlinear
Systems (A13.2), as well as numerical difficulties due to loss of feasibility (A13.3) and slow or no progress due to
stalling (A13.4).
A3
Iteration 0: The Initial Point
The first few ”iterations” in the iteration log (see section 2 in the main text for an example) are special initialization
iterations, but they have been counted as real iterations to allow the user to interrupt at various stages during
initialization. Iteration 0 corresponds to the input point exactly as it was received from GAMS. The sum of
infeasibilities in the column labeled ”Infeasibility” includes all residuals, also from the objective constraint where
”Z =E= expression” will give rise to the term abs( Z - expression ) that may be nonzero if Z has not been
initialized. You may stop CONOPT after iteration 0 with ”OPTION ITERLIM = 0;” in GAMS. The solution
returned to GAMS will contain the input point and the values of the constraints in this point. The marginals of
both variables and equations have not yet been computed and they will be returned as EPS.
This possibility can be used for debugging when you have a reference point that should be feasible, but is
infeasible for unknown reasons. Initialize all variables to their reference values, also all intermediated variables,
and call CONOPT with ITERLIM = 0. Then compute and display the following measures of infeasibility for
each block of constraints, represented by the generic name EQ:
=E= constraints: ROUND(ABS(EQ.L - EQ.LO),3)
=L= constraints: ROUND(MIN(0,EQ.L - EQ.UP),3)
=G= constraints: ROUND(MIN(0,EQ.LO - EQ.L),3)
The ROUND function rounds to 3 decimal places so GAMS will only display the infeasibilities that are larger
than 5.e-4.
Similar information can be derived from inspection of the equation listing generated by GAMS with ”OPTION
LIMROW = nn;”, but although the method of going via CONOPT requires a little more work during implementation
it can be convenient in many cases, for example for large models and for automated model checking.
A4
Iteration 1: Preprocessing
Iteration 1 corresponds to a pre-processing step. Constraints-variable pairs that can be solved a priori (so-called
pre-triangular equations and variables) are solved and the corresponding variables are assigned their final values.
Constraints that always can be made feasible because they contain a free variable with a constant coefficient
(so-called post-triangular equation-variable pairs) are excluded from the search for a feasible solution, and from
the Infeasibility measure in the iteration log. Implicitly, the equations and variables are ordered as shown in Fig.
7.1.
A4.1 Preprocessing: Pre-triangular Variables and Constraints
The pre-triangular equations are those labeled A in Fig.7.1 . They are solved one by one along the ”diagonal”
with respect to the pre-triangular variables labeled I. In practice, GAMS/CONOPT looks for equations with only
one non-fixed variable. If such an equation exists, GAMS/CONOPT tries to solve it with respect to this non-fixed
variable. If this is not possible the overall model is infeasible, and the exact reason for the infeasibility is easy
to identify as shown in the examples below. Otherwise, the final value of the variable has been determined, the
variable can for the rest of the optimization be considered fixed, and the equation can be removed from further
consideration. The result is that the model has one equation and one non-fixed variable less. As variables are
fixed new equations with only one non-fixed variable may emerge, and CONOPT repeats the process until no
more equations with one non-fixed variable can be found.
This pre-processing step will often reduce the effective size of the model to be solved. Although the pre-triangular
variables and equations are removed from the model during the optimization, CONOPT keeps them around until