A Direct Approach for Solving Generalized Geometric Programming Problems: Another Illustration
Jsun Yui Wong
Similar to the computer programs of the preceding paper, the computer program listed below seeks to solve Example 1 of Lu [55, pp. 444-445] :
Minimize
X(1) + 2 * X(2) + X(3)
subject to
X(1) ^ .3 * X(2) ^ -4 * X(3) ^ .8 - .5 * X(1) + .8 * X(2) - .6 * X(3) <= 0
X(1) - X(2) + X(3) <= 2
X(1) + X(2) - X(3) = 0
.1 <= X(i) <=10, i=1, 2, 3.
0 REM DEFDBL A-Z
1 REM DEFINT I, J, K
2 DIM B(99), N(99), A(200), H(99), L(99), U(99), X(200), D(111), P(111), PS(33), J(99), AA(99), HR(32), HHR(32), LHS(44), PLHS(44), LB(22), UB(22), PX(44), J44(44), PN(22), NN(22)
9 FOR JJJJ = -32000 TO 32000
89 RANDOMIZE JJJJ
90 M = -3D+30
95 FOR J44 = 1 TO 3
97 A(J44) = .1 + RND * 9.9
99 NEXT J44
128 FOR I = 1 TO 50000
129 FOR KKQQ = 1 TO 3
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
139 FOR IPP = 1 TO FIX(1 + RND * 2)
140 B = 1 + FIX(RND * 3)
146 IF RND < .5 THEN 160 ELSE GOTO 167
160 R = (1 - RND * 2) * A(B)
164 X(B) = A(B) + (RND ^ (RND * 15)) * R
165 GOTO 188
167 IF RND < .5 THEN X(B) = A(B) - FIX(RND * 4) ELSE X(B) = A(B) + FIX(RND * 4)
188 NEXT IPP
214 FOR J44 = 1 TO 3
217 IF X(J44) < .1 THEN 1670
218 IF X(J44) > 10 THEN 1670
219 NEXT J44
283 X(1) = -X(2) + X(3)
285 IF X(1) - X(2) + X(3) > 2 THEN 1670
286 IF X(1) < 0 THEN 1670
287 IF X(1) ^ .3 * X(2) ^ -4 * X(3) ^ .8 - .5 * X(1) + .8 * X(2) - .6 * X(3) > 0 THEN 1670
480 PD1 = -X(1) - 2 * X(2) - X(3)
484 P = PD1
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 3
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1670 NEXT I
1677 IF M < -999999999999 THEN 1999
1904 PRINT A(1), A(2), A(3), M, JJJJ
1999 NEXT
This computer program was run with qb64v1000-win [101]. Its complete output of one run through JJJJ= -31988 is shown below:
.6773492 1.346448 2.023797 -5.394041 -32000
.7023027 1.330347 2.032649 -5.395645 -31999
.7161303 1.322715 2.038301 -5.396785 -31998
.6693304 1.35204 2.02137 -5.394779 -31997
.7168598 1.321757 2.038617 -5.398991 -31995
.6927465 1.336294 2.029041 -5.394376 -31993
.6840969 1.341907 2.026004 -5.393915 -31992
.7335927 1.31252 2.046113 -5.404746 -31991
.7439328 1.017121 2.051054 -5.409228 -31990
.6979746 1.333008 2.030983 -5.394974 -31989
.6831414 1.342541 2.025683 -5.393907 -31988
Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. On a personal computer with Processor Intel Pentium CPU G620@ 2.60GHz, 4.00 GB of RAM, 64-bit Operating System, and QB64v1000-win [101], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31988 was 3 seconds, counting from "Starting program...". One can compare the computational results above with those in Lu [55, pp. 444-445].
Acknowledgement
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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