MESTRADO EM MODELAGEM COMPUTACIONAL DE CONHECIMENTO

GAMS Rev 116  Windows NT/95/98                    11/03/04 10:33:23  PAGE      1

o problema de pnl com programacao quadratica

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

      problema, atraves de um exemplo, que possa otimizar uma funcao quadratica em x

      enquanto as restricoes sao funcoes lineares em x. Para implementar empregamos

      um pacote  de otimizacao matematica chamado GAMS.

   8  positive variables

   9  x1

  10  x2;

  11

  12  variables

  13

  14  z funcao objetivo;

  15

  16  equations

  17  q1 funcao g(x)

  18  q2 funcao objetivo

  19  q3 x1

  20  q4 x2;

  21

  22

  23  q1.. -x1 - x2 + 3 =g=0;

  24  q2.. x1*x1 + x2*x2 =e=z;

  25  q3.. x1 =g=0;

  26  q4.. x2 =g=0;

  27

  28  x1.l=1;

  29  x2.l=2;

  30

  31  option NLP=CONOPT2;

  32  model pnlprogramacaoquadratica /all/;

  33  solve pnlprogramacaoquadratica using NLP maximize z;

COMPILATION TIME     =        0.000 SECONDS    0.7 Mb      WIN194-116

GAMS Rev 116  Windows NT/95/98                    11/03/04 10:33:23  PAGE      2

o problema de pnl com programacao quadratica

Equation Listing    SOLVE pnlprogramacaoquadratica USING NLP FROM LINE 33

---- q1  =G=  funcao g(x)

q1..  - x1 - x2 =G= -3 ; (LHS = -3)

---- q2  =E=  funcao objetivo

q2..  (2)*x1 + (4)*x2 - z =E= 0 ; (LHS = 5, INFES = 5 ***)

---- q3  =G=  x1

q3..  x1 =G= 0 ; (LHS = 1)

---- q4  =G=  x2

q4..  x2 =G= 0 ; (LHS = 2)

GAMS Rev 116  Windows NT/95/98                    11/03/04 10:33:23  PAGE      3

o problema de pnl com programacao quadratica

Column Listing      SOLVE pnlprogramacaoquadratica USING NLP FROM LINE 33

---- x1

x1

                (.LO, .L, .UP = 0, 1, +INF)

       -1       q1

       (2)      q2

        1       q3

---- x2

x2

                (.LO, .L, .UP = 0, 2, +INF)

       -1       q1

       (4)      q2

        1       q4

---- z  funcao objetivo

z

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

       -1       q2

GAMS Rev 116  Windows NT/95/98                    11/03/04 10:33:23  PAGE      4

o problema de pnl com programacao quadratica

Model Statistics    SOLVE pnlprogramacaoquadratica USING NLP FROM LINE 33

MODEL STATISTICS

BLOCKS OF EQUATIONS       4     SINGLE EQUATIONS        4

BLOCKS OF VARIABLES       3     SINGLE VARIABLES        3

NON ZERO ELEMENTS         7     NON LINEAR N-Z          2

DERIVATIVE POOL           6     CONSTANT POOL           0

CODE LENGTH              26

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 10:33:23  PAGE      5

o problema de pnl com programacao quadratica

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

     MODEL   pnlprogramacaoquadratica   OBJECTIVE  z

     TYPE    NLP                        DIRECTION  MAXIMIZE

     SOLVER  CONOPT2                    FROM LINE  33

**** SOLVER STATUS     1 NORMAL COMPLETION

**** MODEL STATUS      2 LOCALLY OPTIMAL

**** OBJECTIVE VALUE                9.0000

 RESOURCE USAGE, LIMIT          0.051     1000.000

 ITERATION COUNT, LIMIT         4        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                       0.020 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            -3.000    -3.000     +INF     -6.000

---- EQU q2              .         .         .       -1.000

---- EQU q3              .         .        +INF       .

---- EQU q4              .        3.000     +INF       .

  q1  funcao g(x)

  q2  funcao objetivo

  q3  x1

  q4  x2

                       LOWER     LEVEL     UPPER    MARGINAL

---- VAR x1              .         .        +INF     -6.000

---- VAR x2              .        3.000     +INF       .

---- VAR z              -INF      9.000     +INF       .

  x1

  x2

  z  funcao objetivo

GAMS Rev 116  Windows NT/95/98                    11/03/04 10:33:23  PAGE      6

o problema de pnl com programacao quadratica

**** REPORT SUMMARY :        0     NONOPT

                             0 INFEASIBLE

                             0  UNBOUNDED

                             0     ERRORS

EXECUTION TIME       =        0.050 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\PNLEXERC3.GMS

OUTPUT     C:\DOCUMENTS AND SETTINGS\ADMINISTRADOR\DESKTOP\ALLAN\PNLEXERC3.LST