MESTRADO EM MODELAGEM COMPUTACIONAL DE CONHECIMENTO

GAMS Rev 116  Windows NT/95/98                    11/03/04 10:53:33  PAGE      1

o problema de pnl com programacao geometrica

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

      problema, atraves de um exemplo, que possa otimizar uma funcao objetivo e as

      restricoes sao funcoes posinomais (uma extensao do conceito de polinomiais).

      Para implementar empregamos um pacote  de otimizacao matematica chamado GAMS.

   8  variables

   9  x1

  10  x2;

  11

  12  variables

  13

  14  z funcao objetivo;

  15

  16

  17  equations

  18  q1 funcao g1(x)

  19  q2 funcao g2(x)

  20  q3 funcao objetivo;

  21

  22

  23

  24

  25  q1.. -x1*x1 - x2*x2 + 9 =g=0;

  26  q2.. -x1 - x2 + 1 =g=0;

  27  q3.. x1*x1 + x2 =e=z;

  28

  29

  30  option NLP=CONOPT2;

  31  model pnlprogramacaogeometrica /all/;

  32  solve pnlprogramacaogeometrica using NLP minimize z;

COMPILATION TIME     =        0.000 SECONDS    0.7 Mb      WIN194-116

GAMS Rev 116  Windows NT/95/98                    11/03/04 10:53:33  PAGE      2

o problema de pnl com programacao geometrica

Equation Listing    SOLVE pnlprogramacaogeometrica USING NLP FROM LINE 32

---- q1  =G=  funcao g1(x)

q1..  (0)*x1 + (0)*x2 =G= -9 ; (LHS = 0)

---- q2  =G=  funcao g2(x)

q2..  - x1 - x2 =G= -1 ; (LHS = 0)

---- q3  =E=  funcao objetivo

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

GAMS Rev 116  Windows NT/95/98                    11/03/04 10:53:33  PAGE      3

o problema de pnl com programacao geometrica

Column Listing      SOLVE pnlprogramacaogeometrica USING NLP FROM LINE 32

---- x1

x1

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

       (0)      q1

       -1       q2

       (0)      q3

---- x2

x2

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

       (0)      q1

       -1       q2

        1       q3

---- z  funcao objetivo

z

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

       -1       q3

GAMS Rev 116  Windows NT/95/98                    11/03/04 10:53:33  PAGE      4

o problema de pnl com programacao geometrica

Model Statistics    SOLVE pnlprogramacaogeometrica USING NLP FROM LINE 32

MODEL STATISTICS

BLOCKS OF EQUATIONS       3     SINGLE EQUATIONS        3

BLOCKS OF VARIABLES       3     SINGLE VARIABLES        3

NON ZERO ELEMENTS         7     NON LINEAR N-Z          3

DERIVATIVE POOL           6     CONSTANT POOL           0

CODE LENGTH              44

GENERATION TIME      =        0.070 SECONDS    1.9 Mb      WIN194-116

EXECUTION TIME       =        0.070 SECONDS    1.9 Mb      WIN194-116

GAMS Rev 116  Windows NT/95/98                    11/03/04 10:53:33  PAGE      5

o problema de pnl com programacao geometrica

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

     MODEL   pnlprogramacaogeometrica   OBJECTIVE  z

     TYPE    NLP                        DIRECTION  MINIMIZE

     SOLVER  CONOPT2                    FROM LINE  32

**** SOLVER STATUS     1 NORMAL COMPLETION

**** MODEL STATUS      2 LOCALLY OPTIMAL

**** OBJECTIVE VALUE               -3.0000

 RESOURCE USAGE, LIMIT          0.109     1000.000

 ITERATION COUNT, LIMIT        12        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. Reduced gradient less than tolerance.

 CONOPT time Total                       0.078 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            -9.000    -9.000     +INF      0.167

---- EQU q2            -1.000     3.000     +INF       EPS

---- EQU q3              .         .         .       -1.000

  q1  funcao g1(x)

  q2  funcao g2(x)

  q3  funcao objetivo

                       LOWER     LEVEL     UPPER    MARGINAL

---- VAR x1             -INF  -2.01E-13     +INF       .

---- VAR x2             -INF     -3.000     +INF       .

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

  x1

  x2

  z  funcao objetivo

GAMS Rev 116  Windows NT/95/98                    11/03/04 10:53:33  PAGE      6

o problema de pnl com programacao geometrica

**** 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\PNLEXERC4.GMS