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CONOPT 135
E2 is solved with respect to
X2. Solution value = 6.0000000000E-01
E1 could not be solved with respect to
X1. Final solution value = 3.0000000000E+00
E1 remains infeasible with residual = 9.8612288668E-02
The problem is as indicated that the variable to be solved for is at a bound, and the value suggested by Newton’s
method is on the infeasible side of the bound. The critical variable is X1 and the critical equation is E1, i.e.
X1 tries to exceed its bound when CONOPT solves equation E1 with respect to X1. To help you analyze the
problem, especially for larger models, CONOPT reports the solution sequence that led to the infeasibility: In this
case equation E2 was first solved with respect to variable X2, then equation E1 was attempted to be solved with
respect to X1 at which stage the problem appeared. To make the analysis easier CONOPT will always report the
minimal set of equations and variables that caused the infeasibility.
Another type of infeasibility is shown by the following model:
VARIABLE X1, X2, X3, OBJ;
EQUATION E1, E2, E3;
E1 .. SQR(X1) + X2 =E= 1.6;
E2 .. 5 * X2 =E= 3;
E3 .. OBJ =E= SQR(X1) + 2 * SQR(X2) + 3 * SQR(X3);
MODEL DEMO / ALL /; SOLVE DEMO USING NLP MINIMIZING OBJ;
where LOG(X1) has been replaced by SQR(X1) and the lower bound on X1 has been removed. This model gives
the message:
** An equation in the pre-triangular part of the model cannot
be solved because of too small pivot.
Adding a bound or initial value may help.
Residual= 4.0000000
Tolerance (RTNWTR)= 6.34931126E-07
E1: Infeasibility in pre-triangular part of model.
X1: Infeasibility in pre-triangular part of model.
The solution order of the critical equations and
variables is:
E2 is solved with respect to
X2. Solution value = 6.0000000000E-01
E1 could not be solved with respect to
X1. Final solution value = 0.0000000000E+00
E1 remains infeasible with residual =-4.0000000000E+00
After equation E2 has been solved with respect to X2, equation E1 that contains the term X1 2 should be solved
with respect to X1. The initial value of X1 is the default value zero. The derivative of E1 with respect to X1 is
therefore zero, and it is not possible for CONOPT to determine whether to increase or decrease X1. If X1 is given
a nonzero initial value the model will solve. If X1 is given a positive initial value the equation will give X1 = 1,
and if X1 is given a negative initial value the equation will give X1 = -1. The last type of infeasibility that can
be detected during the solution of the pre-triangular or recursive equations is shown by the following example
VARIABLE X1, X2, X3, OBJ;