The computer program listed below seeks to solve the following nonlinear programming formulation from page 452 of Lu [14]:
Minimize .622 * X(1) * X(3) * X(4) + 1.7781 * X(2) * X(3) ^ 2 + 3.1661 * X(1) ^ 2 * X(4) + 19.84 * X(1) ^ 2 * X(3)
subject to
-X(1)+ .0193 * X(3)<=0,
- X(2) + .00954 * X(3)<=0,
1296000 - 3.141592654 * X(3) ^ 2 * X(4) - (4 / 3) * 3.141592654 * X(3) ^ 3<=0,
- 240+ X(2)<=0,
.0625<=X(i) <= 6.1875, i=1, 2,
10<=X(3) <= 200, i=3, 4.
X(1) through X(4) are continuous.
X(5) through X(8) below are slack variables.
0 DEFDBL A-Z
2 DEFINT K
3 DIM B(199), N(199), A(199), H(199), L(199), U(199), X(1111), D(111), P(111), PS(133)
12 FOR JJJJ = -32000 TO 32000 STEP .01
14 RANDOMIZE JJJJ
16 M = -1D+37
22 FOR J55 = 1 TO 2
67 A(J55) = .0625 + RND * 6.125
71 NEXT J55
82 FOR J55 = 3 TO 4
86 A(J55) = 10 + RND * 190
88 NEXT J55
128 FOR I = 1 TO 60000
129 FOR KKQQ = 1 TO 4
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
132 REM GOTO 163
133 FOR IPP = 1 TO (1 + FIX(RND * 4))
151 J = 1 + FIX(RND * 4)
153 r = (1 - RND * 2) * A(J)
157 X(J) = A(J) + (RND ^ (RND * 10)) * r
161 NEXT IPP
163 REM
164 REM
197 IF X(1) < .0625 THEN 1670
199 IF X(1) > 6.1875 THEN 1670
201 IF X(2) < .0625 THEN 1670
203 IF X(2) > 6.1875 THEN 1670
205 IF X(3) < 10 THEN 1670
207 IF X(3) > 200 THEN 1670
209 IF X(4) < 10 THEN 1670
211 IF X(4) > 200 THEN 1670
261 X(5) = X(1) - .0193 * X(3)
264 X(6) = X(2) - .00954 * X(3)
267 X(7) = -1296000 + 3.141592654 * X(3) ^ 2 * X(4) + (4 / 3) * 3.141592654 * X(3) ^ 3
269 X(8) = 240 - X(2)
281 FOR J99 = 5 TO 8
283 IF X(J99) < 0 THEN X(J99) = X(J99) ELSE X(J99) = 0
285 NEXT J99
365 POBA = -.622 * X(1) * X(3) * X(4) - 1.7781 * X(2) * X(3) ^ 2 - 3.1661 * X(1) ^ 2 * X(4) - 19.84 * X(1) ^ 2 * X(3) + 1000000 * (X(8) + X(7) + X(6) + X(5))
466 P = POBA
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 8
1459 A(KLX) = X(KLX)
1460 NEXT KLX
1557 REM GOTO 128
1670 NEXT I
1889 IF M < -5884.5 THEN 1999
1900 PRINT A(1), A(2), A(3), A(4), A(5)
1911 PRINT A(6), A(7), A(8), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with qb64v1000-win [27]. The complete output through JJJJ = -31951.60000000775 is shown below:
.7791371869593762 .3851279152120704 40.36980243312682
199.3025835450308 0
0 0 0 -5884.48288302348
-31993.1700000011
.7785102423305716 .38481801615722 40.33731825546528
199.7537562076116 0
0 0 0 -5883.4077896634
-31951.60000000775
Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. The computational results above can be compared with the results in Table 7 of Lu [14, p. 453].
On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM and qb64v1000-win [27], the wall-clock time for obtaining the output through
JJJJ= -31951.60000000775 was 10 minutes, total.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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