| Name: |
Sixeq1 - Poorly scaled chemical
equilibrium problem |
| Source: |
Hiebert, K. L., ACM Trans.
Math. Software 8, 1(1982) |
| Reference/s |
Bullard, L. G. and Biegler,
L. T., Computers Chem. Engng. 15(4), 239 (1991). |
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| Model: |
6 implicit equations, indep.
variables x1 to x6 |
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Higher difficulty level |
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Constraints: xi are nonnegative
for I=1,2,…6 |
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Discontinuities: none |
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Initial estimates: 1. (10,10,10,10,10,10);
2.(1,1,1,1,1,1); |
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3. (0,0,0,0,0,0); 4. (1e-4,1e-3,0,1e-4,55,1e-4) |
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| Solved by |
Shacham, M., POLYMATH 5.1,
build 19, April 6, 2001 |
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| Model Eqs. |
Poorly scaled chemical equilibrium
problem |POLVER05_3 |
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EXCEL
FILE |
f(x1) = x1+x2+x4-0.001 # |
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TEXT
FILE |
f(x2) = x5+x6-55 # |
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POLYMATH
FILE |
f(x3) = x1+x2+x3+2*x5+x6-110.001
# |
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f(x4) = x1-0.1*x2 # |
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f(x5) = x1-1e4*x3*x4 # |
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f(x6) = x5-55e14*x3*x6 # |
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x1(0)=10 |
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x2(0)=10 |
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x3(0)=10 |
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x4(0)=10 |
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x5(0)=10 |
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x6(0)=10 |
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| Variable/function values |
Variable |
Value |
f(x) |
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x1 |
10 |
29.999 |
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x2 |
10 |
-35 |
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x3 |
10 |
-50.001 |
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x4 |
10 |
9 |
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x5 |
10 |
-999990 |
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x6 |
10 |
-5.50E+17 |
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| Solution |
Variable |
Value |
f(x) |
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x1 |
0.0000826446329 |
0 |
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x2 |
0.0008264463286 |
0 |
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x3 |
0.0000909091485 |
0 |
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x4 |
0.0000909090385 |
0 |
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x5 |
54.9999999998900 |
0 |
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x6 |
0.0000000001100 |
-7.5318E-13 |
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| Infeasible solution |
Variable |
Value |
f(x) |
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x1 |
-0.0000000001000 |
0 |
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x2 |
-0.0000000010000 |
0 |
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x3 |
-0.0000000000100 |
0 |
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x4 |
0.0010000000000 |
0 |
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x5 |
55.0010000000000 |
-5.17E-26 |
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x6 |
-0.0010000000000 |
2.1320E-14 |
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| Additional information |
There is a serious scaling
problem in this example (see the |
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order of magnitude of the
function values at the initial guess) |
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Error tolerances on x must
be set at a very small value to |
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prevent premature stop of
the iterations. Most algorithms |
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will converge to the infeasible
solution or won't converge |
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when started from initial
quesses 3 and 4. |