Similar to the computer programs of the preceding papers, the computer program below seeks to solve Li and Sun's Problem 14.5, [12, p. 416], but with an additional less-than-or-equal-to constraint and with 10000 unknowns instead of 100 unknowns. Specifically, the test example here is as follows:
Minimize
10000 10000
SIGMA X(i)^4 + [ SIGMA X(i) ]^2
i=1 i=1
subject to
X(1)^2+X(2)^2+X(3)^2+...+X(10000)^2 <= 10000
-5<=X(i)<=5, X(i) integer, i=1, 2, 3,..., 10000.
One notes line 83 through line 87 and line 170 through line 173.
The present paper uses the IBM Personal Computer BASIC Compiler--through A:\>bascom and A:\>link--Copyright IBM Corp 1982 Version 1.00/Copyright Microsoft, Inc. 1982.
0 DEFINT J,K,B,X
2 DIM A(10001),X(10001)
81 FOR JJJJ=-32000 TO 32000
83 LB=-FIX(RND*6)
87 UB=FIX(RND*6)
89 RANDOMIZE JJJJ
90 M=-1.5D+38
111 FOR J44=1 TO 10000
114 IF RND<.5 THEN A(J44)=0 ELSE A(J44)=1
117 NEXT J44
128 FOR I=1 TO 32000
129 FOR KKQQ=1 TO 10000
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
139 FOR IPP=1 TO FIX(1+RND*.3)
140 B=1+FIX(RND*10000)
167 IF RND<.5 THEN X(B)=(A(B)-1) ELSE X(B)=(A(B) +1 )
169 NEXT IPP
170 FOR J44=1 TO 10000
171 IF X(J44)<LB THEN X(J44 )=A(J44 )
172 IF X(J44)>UP THEN X(J44 )=A(J44 )
173 NEXT J44
174 SUMNEW=0
175 FOR J44=1 TO 10000
176 SUMNEW=SUMNEW+X(J44) ^2
177 NEXT J44
178 X(10001)=10000- SUMNEW
179 IF X(10001)<0 THEN X(10001)=X(10001) ELSE X(10001)=0
182 SUMY=0
183 FOR J44=1 TO 10000
185 SUMY=SUMY+X(J44)^4
187 NEXT J44
200 SUMNEWZ=0
203 FOR J44=1 TO 10000
205 SUMNEWZ=SUMNEWZ+ X(J44)
207 NEXT J44
689 PD1=-SUMY-SUMNEWZ^2 +50000!*X(10001)
1111 IF PD1<=M THEN 1670
1452 M=PD1
1454 FOR KLX=1 TO 10001
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1559 GOTO 128
1670 NEXT I
1953 PRINT A(1),A(2),A(3),A(4),A(5)
1965 PRINT A(7996),A(7997),A(7998),A(7999),A(8000)
1966 PRINT M,JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with the IBM Personal Computer BASIC Compiler, Version 1.00. See the BASIC manual [11, page iii, Preface]. Copied by hand from the screen, the computer program's complete output through JJJJ=-31996 is shown below:
0 -1 -1 -1 0
0 -1 0 -1 -1
-5610 -32000
-1 0 -1 -1 -1
0 0 1 -1 1
-4984 -31999
0 0 0 0 0
0 0 0 0 0
0 -31998
-1 0 0 -1 0
0 0 0 0 0
-5564 -31997
0 0 0 0 0
0 0 0 0 0
0 -31996
Above there is no rounding by hand; it is just straight copying by hand from the screen.
M=0 is optimal. See Li and Sun [12, p. 416].
Of the 10000 A's, only the 10 A's of line 1953 through line 1965 are shown above.
On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM, and the IBM Personal Computer BASIC Compiler, Copyright IBM Corp 1982 Version 1.00/Copyright Microsoft, Inc. 1982, the wall-clock time for obtaining the output through JJJJ=-31996 was three hours.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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