The computer program listed below seeks to solve the following problem from page 710 of Li and Lu [9, Program 3].
Minimize X(1) ^ 3 * X(2) * X(3) ^ 3 * X(4) + X(1) ^ 3 * X(2) * X(3) * X(4) ^ 2
subject to
X(1) ^ 3 * X(2) * X(3) ^ 2 + X(3) * X(4)<=-500,
- X(1) ^ 3 * X(2) * X(3) + X(3) ^ 2 * X(4)<=500,
-5<=X(1) <=5,
-5<=X(2) <=5,
where
X(3) Epsilon{ -1, 0, 1, 4, 5, 6, 7.5, 8, 9, 10 },
X(4) Epsilon{ -27, -18, -9, -7, -4, -1, 1, 3, 4, 5 }.
The added variables X(5) and X(6) below are slack variables. One takes note of line 330, which is 330 IF X(J99) < 0 THEN X(J99) = X(J99) ELSE X(J99) = 0.
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
75 A(1) = -5 + RND * 10
77 A(2) = -5 + RND * 10
86 IF RND < .100 THEN A(3) = -1 ELSE IF RND < .111 THEN A(3) = 0 ELSE IF RND < .125 THEN A(3) = 1 ELSE IF RND < .143 THEN A(3) = 4 ELSE IF RND < .167 THEN A(3) = 5 ELSE IF RND < .200 THEN A(3) = 6 ELSE IF RND < .25 THEN A(3) = 7.5 ELSE IF RND < .333 THEN A(3) = 8 ELSE IF RND < .5 THEN A(3) = 9 ELSE A(3) = 10
88 IF RND < .100 THEN A(4) = -27 ELSE IF RND < .111 THEN A(4) = -28 ELSE IF RND < .125 THEN A(4) = -9 ELSE IF RND < .143 THEN A(4) = -7 ELSE IF RND < .167 THEN A(4) = -4 ELSE IF RND < .200 THEN A(4) = -1 ELSE IF RND < .25 THEN A(4) = 1 ELSE IF RND < .333 THEN A(4) = 3 ELSE IF RND < .5 THEN A(4) = 4 ELSE A(4) = 5
128 FOR I = 1 TO 3000
129 FOR KKQQ = 1 TO 4
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
133 FOR IPP = 1 TO (1 + FIX(RND * 1))
134 r = (1 - RND * 2) * A(1)
135 IF RND < .5 THEN 137
136 X(1) = A(1) + (RND ^ (RND * 10)) * r
137 IF RND < .5 THEN 139
138 X(2) = A(2) + (RND ^ (RND * 10)) * r
139 IF RND < .5 THEN 151
141 IF RND < .100 THEN X(3) = -1 ELSE IF RND < .111 THEN X(3) = 0 ELSE IF RND < .125 THEN X(3) = 1 ELSE IF RND < .143 THEN X(3) = 4 ELSE IF RND < .167 THEN X(3) = 5 ELSE IF RND < .200 THEN X(3) = 6 ELSE IF RND < .25 THEN X(3) = 7.5 ELSE IF RND < .333 THEN X(3) = 8 ELSE IF RND < .5 THEN X(3) = 9 ELSE X(3) = 10
151 IF RND < .5 THEN 191
161 IF RND < .100 THEN X(4) = -27 ELSE IF RND < .111 THEN X(4) = -18 ELSE IF RND < .125 THEN X(4) = -9 ELSE IF RND < .143 THEN X(4) = -7 ELSE IF RND < .167 THEN X(4) = -4 ELSE IF RND < .200 THEN X(4) = -1 ELSE IF RND < .25 THEN X(4) = 1 ELSE IF RND < .333 THEN X(4) = 3 ELSE IF RND < .5 THEN X(4) = 4 ELSE X(4) = 5
191 NEXT IPP
208 IF X(1) < -5 THEN 1670
210 IF X(1) > 5 THEN 1670
211 IF X(2) < -5 THEN 1670
212 IF X(2) > 5 THEN 1670
301 X(5) = -500 - X(1) ^ 3 * X(2) * X(3) ^ 2 - X(3) * X(4)
303 X(6) = 500 + X(1) ^ 3 * X(2) * X(3) - X(3) ^ 2 * X(4)
325 FOR J99 = 5 TO 6
330 IF X(J99) < 0 THEN X(J99) = X(J99) ELSE X(J99) = 0
331 NEXT J99
357 POBA = -X(1) ^ 3 * X(2) * X(3) ^ 3 * X(4) - X(1) ^ 3 * X(2) * X(3) * X(4) ^ 2 + 1000000 * (X(5) + X(6))
466 P = POBA
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 6
1459 A(KLX) = X(KLX)
1460 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < 369900 THEN 1999
1900 PRINT A(1), A(2), A(3), A(4)
1901 PRINT A(5), A(6), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with qb64v1000-win [26]. The complete output through JJJJ = -31999.96000000001 is shown below:
-4.958160881457932 4.323632488239245 1
-27
0 0 369953.99999999944 -31999.98
-4.842381486860238 4.64123558725103 1
-27
0 0 369953.99999999944 -31999.97000000001
-4.762515957826314 4.878668210944634 1
-27
0 0 369954 -31999.96000000001
Above there is no rounding by hand; it is just straight copying by hand from the monitor screen.
On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM and qb64v1000-win [26], the wall-clock time for obtaining the output through JJJJ= -31999.96000000001 was 8 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.
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