MESTRADO EM MODELAGEM COMPUTACIONAL DE CONHECIMENTO

GAMS Rev 116  Windows NT/95/98                    11/03/04 09:54:10  PAGE      1

o problema de pnl restrita

      Este problema de programacao nao linear restrita, busca resolver uma situacao

      problema, atraves de um exemplo, que possa otimizar uma funcao com restricoes.

      Para implementar empregamos um pacote  de otimizacao matematica chamado GAMS.

   7  positive variables

   8  x1

   9  x2;

  10

  11  variables

  12

  13  z funcao objetivo;

  14

  15  equations

  16  q1 funcao h(x)

  17  q2 funcao g(x)

  18  q3 funcao objetivo

  19  q4 x1

  20  q5 x2;

  21

  22

  23  q1.. x1*x1 + x2*x2 - 1 =g=0;

  24  q2.. x1 + 2*x2 - 0.5 =g=0;

  25  q3.. x1*x1 + x2*x2 + 2*x2 =e=z;

  26  q4.. x1 =g=0;

  27  q5.. x2 =g=0;

  28

  29  option NLP=CONOPT2;

  30  model pnlrestrita /all/;

  31  solve pnlrestrita using NLP minimizing z;

COMPILATION TIME     =        0.000 SECONDS    0.7 Mb      WIN194-116

GAMS Rev 116  Windows NT/95/98                    11/03/04 09:54:10  PAGE      2

o problema de pnl restrita

Equation Listing    SOLVE pnlrestrita USING NLP FROM LINE 31

---- q1  =G=  funcao h(x)

q1..  (0)*x1 + (0)*x2 =G= 1 ; (LHS = 0, INFES = 1 ***)

---- q2  =G=  funcao g(x)

q2..  x1 + 2*x2 =G= 0.5 ; (LHS = 0, INFES = 0.5 ***)

---- q3  =E=  funcao objetivo

q3..  (0)*x1 + (2)*x2 - z =E= 0 ; (LHS = 0)

---- q4  =G=  x1

q4..  x1 =G= 0 ; (LHS = 0)

---- q5  =G=  x2

q5..  x2 =G= 0 ; (LHS = 0)

GAMS Rev 116  Windows NT/95/98                    11/03/04 09:54:10  PAGE      3

o problema de pnl restrita

Column Listing      SOLVE pnlrestrita USING NLP FROM LINE 31

---- x1

x1

                (.LO, .L, .UP = 0, 0, +INF)

       (0)      q1

        1       q2

       (0)      q3

        1       q4

---- x2

x2

                (.LO, .L, .UP = 0, 0, +INF)

       (0)      q1

        2       q2

       (2)      q3

        1       q5

---- z  funcao objetivo

z

                (.LO, .L, .UP = -INF, 0, +INF)

       -1       q3

GAMS Rev 116  Windows NT/95/98                    11/03/04 09:54:10  PAGE      4

o problema de pnl restrita

Model Statistics    SOLVE pnlrestrita USING NLP FROM LINE 31

MODEL STATISTICS

BLOCKS OF EQUATIONS       5     SINGLE EQUATIONS        5

BLOCKS OF VARIABLES       3     SINGLE VARIABLES        3

NON ZERO ELEMENTS         9     NON LINEAR N-Z          4

DERIVATIVE POOL           6     CONSTANT POOL           8

CODE LENGTH              57

GENERATION TIME      =        0.060 SECONDS    1.9 Mb      WIN194-116

EXECUTION TIME       =        0.060 SECONDS    1.9 Mb      WIN194-116

GAMS Rev 116  Windows NT/95/98                    11/03/04 09:54:10  PAGE      5

o problema de pnl restrita

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

     MODEL   pnlrestrita         OBJECTIVE  z

     TYPE    NLP                 DIRECTION  MINIMIZE

     SOLVER  CONOPT2             FROM LINE  31

**** SOLVER STATUS     1 NORMAL COMPLETION

**** MODEL STATUS      2 LOCALLY OPTIMAL

**** OBJECTIVE VALUE                3.0000

 RESOURCE USAGE, LIMIT          0.109     1000.000

 ITERATION COUNT, LIMIT         6        10000

 EVALUATION ERRORS              0            0

    C O N O P T 2   Wintel  version 2.071D-005-039

    Copyright (C)   ARKI Consulting and Development A/S

                    Bagsvaerdvej 246 A

                    DK-2880 Bagsvaerd , Denmark

 Using default control program.

 ** Optimal solution. There are no superbasic variables.

 CONOPT time Total                       0.082 seconds

   of which: Function evaluations        0.000 =  0.0%

             Derivative evaluations      0.000 =  0.0%

 Work length =    0.05 Mbytes

    Estimate =    0.05 Mbytes

    Max used =    0.04 Mbytes

                       LOWER     LEVEL     UPPER    MARGINAL

---- EQU q1             1.000     1.000     +INF      2.000

---- EQU q2             0.500     2.000     +INF       .

---- EQU q3              .         .         .       -1.000

---- EQU q4              .         .        +INF       .

---- EQU q5              .        1.000     +INF       .

  q1  funcao h(x)

  q2  funcao g(x)

  q3  funcao objetivo

  q4  x1

  q5  x2

                       LOWER     LEVEL     UPPER    MARGINAL

---- VAR x1              .         .        +INF       EPS

---- VAR x2              .        1.000     +INF       .

---- VAR z              -INF      3.000     +INF       .

  x1

GAMS Rev 116  Windows NT/95/98                    11/03/04 09:54:10  PAGE      6

o problema de pnl restrita

  x2

  z  funcao objetivo

**** REPORT SUMMARY :        0     NONOPT

                             0 INFEASIBLE

                             0  UNBOUNDED

                             0     ERRORS

EXECUTION TIME       =        0.000 SECONDS    0.7 Mb      WIN194-116

USER: Joao Inacio Soletti                            G000920:1631AP-WIN

      Universidade Federal de Alagoas, Departamento de EngenhariaDC2982

**** FILE SUMMARY

INPUT      C:\DOCUMENTS AND SETTINGS\ADMINISTRADOR\DESKTOP\ALLAN\PNLEXERC2.GMS

OUTPUT     C:\DOCUMENTS AND SETTINGS\ADMINISTRADOR\DESKTOP\ALLAN\PNLEXERC2.LST