Error in square system: Pivot too small in GAMS model

GAMS
1

I am working on a model and I am encountering the error ‘error in square system: pivot too small’ when I use CNS. When I use NLP, I get a solution but also a message like ‘Optimal solution. Reduced gradient less than tolerance.’ The model I am using is an adaptation of the PEP 1-t model, and it worked fine before I introduced the elements to adapt it for my SAM. I didn’t add or remove any equations or variables. I just added one exogenous variable that allowed for the calibration of government income and the savings of the rest of the world. Can someone please help me find the problem? Here is the summary of the model resolution with CNS:

**** REPORT SUMMARY :        0 INFEASIBLE
                             1  DEPENDENT (DEPND)
                             2     ERRORS ( ****)

BLOCKS OF EQUATIONS         108     SINGLE EQUATIONS        1,699
BLOCKS OF VARIABLES         125     SINGLE VARIABLES        1,699
NON ZERO ELEMENTS         7,201     NON LINEAR N-Z          3,693
CODE LENGTH              10,923     CONSTANT POOL             747
SINGLE =E|X= EQUS         1,699     SINGLE UNFIXED VARS     1,699


GENERATION TIME      =        0.000 SECONDS      8 MB  45.4.0 19dc3313 WEX-WEI
               L O O P S               TIME 10

GAMS 45.4.0  19dc3313 Nov 27, 2023          WEX-WEI x86 64bit/MS Windows - 09/15/24 07:14:23 Page 103
PEP standard model 1-t, version 2.0
Solution Report     SOLVE PEP1T Using CNS From line 2079


               S O L V E      S U M M A R Y

     MODEL   PEP1T               
     TYPE    CNS                 
     SOLVER  CONOPT              FROM LINE  2079

**** SOLVER STATUS     1 Normal Completion
**** MODEL STATUS      17 Solved Singular

 RESOURCE USAGE, LIMIT          0.015 10000000000.000
 ITERATION COUNT, LIMIT         1    2147483647
 EVALUATION ERRORS              0             0
 
 
    C O N O P T 3   version 3.17O
    Copyright (C)   ARKI Consulting and Development A/S
                    Bagsvaerdvej 246 A
                    DK-2880 Bagsvaerd, Denmark
 
 
 ** Warning **  The value of LFITER is out of range.
                LFITER is decreased from 2147483647 to 1000000000.
 
 ** Warning **  The variance of the derivatives in the initial
                point is large (= 5.9 ). A better initial
                point, a better scaling, or better bounds on the
                variables will probably help the optimization.
 
 
                   Pre-triangular equations:   246
                   Post-triangular equations:  20
 
 
 ** Error in Square System: Pivot too small.
 
 
 CONOPT time Total                            0.009 seconds
   of which: Function evaluations             0.007 = 77.8%
             1st Derivative evaluations       0.000 =  0.0%
 

**** ERRORS/WARNINGS IN EQUATION EQ44(10)
     1 error(s): Pivot too small.

**** ERRORS/WARNINGS IN VARIABLE IR(10)
     1 error(s): Pivot too small.

 ---- EQU EQ44  Rest-of-the-world income

         LOWER          LEVEL          UPPER

1          .              .              .     DEPND

      LOWER          LEVEL          UPPER

1        -INF            0.0400        +INF    DEPND
2

Hi @NinaMayers ,

The Conopt3 Manual has some hints on how to interpret the messages you are getting (search e.g. for pivot too small).

I hope this helps!

Fred

3

There are at least 2 dependent equations in your model and the log file indicates it. The problem comes from the choice of exogenous and endogenous variables. You have to check it. You can try to solve the equations one by one insuring that each variable is computed in a unique equation.

Best regards

4

Thanks, I will look this manual