Computer program for completely solving posynomial geometric programming problems: another illustration
Jsun Yui Wong
Similar to the computer program of the preceding paper, the computer program listed below aims to solve directly the following geometric programming problem in Tsai and Lin [92, Example 3, p. 489]:
Minimize
X(1) ^ .4 - X(2) ^ 2
subject to
X(1) ^ 1.85 - 6 * X(1)+ X(2) ^ 2<= 5
X(1) + X(2) <= 8
1 <= X(i) <= 7.4, i = 1, 2.
One notes line 175, which is 175 X(2) = (-X(1) ^ 1.85 + 6 * X(1) + 5) ^ (.5).
0 DEFDBL A-Z
1 REM DEFINT I, J, K
2 DIM B(99), N(99), A(2002), H(99), L(99), U(99), X(2002), 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)
85 FOR JJJJ = -32000 TO 32000
89 RANDOMIZE JJJJ
90 M = -3D+30
115 FOR J44 = 1 TO 2
117 A(J44) = 1 + (RND * 6.4)
122 NEXT J44
128 FOR i = 1 TO 10000
129 FOR KKQQ = 1 TO 2
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
139 FOR IPP = 1 TO FIX(1 + RND * 2)
140 B = 1 + FIX(RND * 2)
144 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 168
167 IF RND < .5 THEN X(B) = A(B) - FIX(RND * 2) ELSE X(B) = A(B) + FIX(RND * 2)
168 NEXT IPP
171 FOR J44 = 1 TO 2
172 IF X(J44) < 1 THEN 1670
173 IF X(J44) > 7.4 THEN 1670
174 NEXT J44
175 X(2) = (-X(1) ^ 1.85 + 6 * X(1) + 5) ^ (.5)
177 IF X(1) + X(2) > 8 THEN 1670
201 FOR J44 = 1 TO 2
203 IF X(J44) < 1 THEN 1670
205 IF X(J44) > 7.4 THEN 1670
207 NEXT J44
561 PD1 = -(X(1) ^ .4 - X(2) ^ 2)
569 P = PD1
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 2
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1670 NEXT i
1775 IF M < -9999999999 THEN 1999
1904 PRINT A(1), A(2), M, JJJJ
1999 NEXT JJJJ
This computer program was run with qb64v1000-win [103]. Its complete output of one run through JJJJ= -31999 is shown below:
3.852641638614181 3.998954891187267 14.27648493768223
-32000
3.852641620521863 3.998954890784436 14.27648493768223
-31999
Above there is no rounding by hand; it is just straight copying by hand from the monitor sticreen. On a personal computer with QB64v1000-win [103], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31999 was 2 seconds, counting from "Starting program...". One can compare the computational results above with the those in Tsai and Lin [92, Example 3].
The computational results presented above were obtained from the following computer system:
Processor: Intel (R) Core (TM) i5 CPU M 430 @2.27 GHz 2.26 GHz
Installed memory (RAM): 4.00GB (3.87 GB usable)
System type: 64-bit Operating System.
Acknowledgement
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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