Solving a nonlinear programming problem from the literature: another test problem in Visweswaran and Floudas [101]

Jsun Yui Wong

Similar to the computer program of the preceding paper, the computer program listed below attempts to solve the following test problem from Visweswaran and Floudas [101, pp. 1431-1432, Example 8].

Minimize

-12 * X(1) - 7 * X(2) + X(2) ^ 2

subject to

-2 * X(1) ^ 4 + 2 - X(2) =0

0 <= X(1) <= 2

0 <= X(2) <= 3.

0 REM DEFDBL A-Z

1 REM DEFINT I, J, K

2 DIM B(99), N(99), A(2002), G(128), J44(222), 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), PN(22), NN(22)

85 FOR JJJJ = -32000 TO 32000

87 RANDOMIZE JJJJ

88 M = -3D+30

111 A(1) = 0 + RND * 2

112 A(2) = 0 + RND * 3

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)

141 B = 1 + FIX(RND * 2)

142 REM IF RND < .5 THEN 160 ELSE GOTO 167

160 r = (1 - RND * 2) * A(B)

162 X(B) = A(B) + (RND ^ (RND * 15)) * r

164 GOTO 168

167 REM IF RND < .5 THEN X(B) = A(B) - 1 ELSE X(B) = A(B) + 1

168 NEXT IPP

175 REM FOR J44 = 1 TO 6

177 REM X(J44) = INT(X(J44))

179 REM NEXT J44

255 X(2) = -2 * X(1) ^ 4 + 2

453 IF X(1) < 0 THEN 1670

454 IF X(1) > 2 THEN 1670

473 IF X(2) < 0 THEN 1670

484 IF X(2) > 3 THEN 1670

922 PD1 = 12 * X(1) + 7 * X(2) - X(2) ^ 2

999 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

1778 IF M < -999999 THEN 1999

1888 PRINT A(1), A(2), M, JJJJ

1999 NEXT JJJJ

This computer program was run with qb64v1000-win [104]. Its complete output of one run through JJJJ= -31995 is shown below:

**.7175208 1.469524 16.73889 -32000**

.7176438 1.469524 16.73889 -31999

.7176516 1.469501 16.73889 -31998

.7175084 1.469524 16.73889 -31997

.7176572 1.469524 16.73889 -31996

.7177044 1.469524 16.73889 -31995

Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. By using the following computer system and QB64v1000-win [104], the wall-clock time **(not CPU time)** for obtaining the output through JJJJ = -31995 was 2 seconds, counting from "Starting program...". One can compare the computational results above with those in Visweswaran and Floudas [101, pp. 1431-1432, Example 8].

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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