Wednesday, October 25, 2017

Solving a Posynomial Program with the Method of the Present Blog

Jsun Yui Wong

The computer program listed below seeks to solve Example 2 of Lu et al. [11, p. 153]:   

Minimize          X(1) ^ -2 * X(2) ^ -1.5 * X(3) ^ 1.2 * X(4) ^ 3 - 3 * X(3) ^ .5 + X(2) - 4 * X(4)

subject to        0.01<= X(1), X(2), X(3), X(4)<=10.


0 DEFDBL A-Z

2 DEFINT K

3 DIM B(99), N(99), A(99), H(99), L(99), U(99), X(1111), D(111), P(111), PS(33)
12 FOR JJJJ = -32000 TO 32000 STEP .01


    14 RANDOMIZE JJJJ
    16 M = -1D+37

    22 FOR J55 = 1 TO 4


        67 A(J55) = .01 + FIX(RND * 1005) * .01

    71 NEXT J55

    128 FOR I = 1 TO 60000


        129 FOR KKQQ = 1 TO 4

            130 X(KKQQ) = A(KKQQ)
        131 NEXT KKQQ
        133 FOR IPP = 1 TO (1 + FIX(RND * 4))

            181 J = 1 + FIX(RND * 4)

            183 REM r = (1 - RND * 2) * A(J)
            187 REM  X(J) = A(J) + (RND ^ (RND * 10)) * r
            189 X(J) = .01 + FIX(RND * 1005) * .01


        191 NEXT IPP
        200 FOR J44 = 1 TO 4

            201 IF X(J44) < .01 THEN 1670
            203 IF X(J44) > 10 THEN 1670
        255 NEXT J44


        359 POBA = -X(1) ^ -2 * X(2) ^ -1.5 * X(3) ^ 1.2 * X(4) ^ 3 + 3 * X(3) ^ .5 - X(2) + 4 * X(4)


        466 P = POBA

        1111 IF P <= M THEN 1670


        1452 M = P
        1454 FOR KLX = 1 TO 4


            1459 A(KLX) = X(KLX)
        1460 NEXT KLX
        1557 REM GOTO 128

    1670 NEXT I

    1889 REM IF M < -.7346 THEN 1999
    1900 PRINT A(1), A(2), A(3), A(4), M, JJJJ

1999 NEXT JJJJ


This BASIC computer program was run with qb64v1000-win [24]. The complete output through JJJJ = -31999.97000000001 is shown below:

10      .32      .01      10      39.76007478129893
-32000

10      .32      .01      10      39.76007478129893
-31999.99

10      .32      .01      10      39.76007478129893
-31999.98

10      .32      .01      10      39.76007478129893
-31999.97000000001

Above there is no rounding by hand; it is just straight copying by hand from the monitor screen.  One can compare the computational results above to the results in Lu et al. [11, Table 1, p. 153].

On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM and qb64v1000-win [24], the wall-clock time for obtaining the output through JJJJ=-31999.97000000001 was 15 seconds; most of these seconds were for creating the .EXE file.     

Acknowledgment

I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.

References

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