Direct Solution of Generalized Geometric Programming Problems: Another Illustration
Jsun Yui Wong
Similar to the computer program of the preceding paper, the computer program listed below seeks to solve the following motivating example in Maranas and Floudas [57, p. 20]:
Minimize
X(1)
subject to
(1/4)*X(1) +(1/2)*X(2)- (1/16)*X(1)^2-(1/16)*X(2)^2-1 <=0
(1/14)*X(1)^2 +(1/14)*X(2)^2 +1 - (3/7)*X(1)-(3/7)*X(2) <=0
1 <= X(1) <=5.5
1 <= X(2) <=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
111 FOR J44 = 1 TO 2
112 A(J44) = 1 + RND * 4.5##
113 NEXT J44
128 FOR I = 1 TO 50000
129 FOR KKQQ = 1 TO 2
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
139 FOR IPP = 1 TO FIX(1 + RND * 1.3)
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) - 1 ELSE X(B) = A(B) + 1
168 NEXT IPP
171 FOR J44 = 1 TO 2
173 IF X(J44) < 1## THEN 1670
175 IF X(J44) > 5.5## THEN 1670
176 NEXT J44
233 IF .25*X(1) +.5*X(2)- (.0625)*X(1)^2-(.0625)*X(2)^2-1 > 0## THEN 1670
236 IF (.07142857142)*X(1)^2 +(.07142857142)*X(2)^2 +1 - (.42857142857)*X(1)-(.42857142857)*X(2) > 0## THEN 1670
344 PD1 = -X(1)
466 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
1777 IF M < -1.18 THEN 1999
1904 PRINT A(1), A(2), M, JJJJ
1999 NEXT JJJJ
This computer program was run with qb64v1000-win [102]. Its output of one run through JJJJ=
-31976 is summarized below:
.
.
.
1.177131573480457 2.177108330198211 -1.177131573480457
-31984
.
.
.
1.178097259693958 2.174973347779237 -1.178097259693958
-31980
.
.
.
1.178113101366557 2.175640793383298 -1.178113101366557
-31976
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 (3.89 GB usable), 64-bit Operating System, and QB64v1000-win [102], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31976 was 3 seconds, counting from "Starting program...". One can compare the computational results above with those in Maranas and Floudas [57, p. 21].
Acknowledgement
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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