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palmer3c.jl
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palmer3c.jl
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# A linear least squares problem
# arising from chemical kinetics.
#
# model: H-N=C=S TZVP+MP2
# fitting Y to A0 + A2 X**2 + A4 X**4 + A6 X**6 + A8 X**8 +
# A10 X**10 + A12 X**12 + A14 X**14
#
# Source:
# M. Palmer, Edinburgh, private communication.
#
# classification QUR2-RN-8-0
export palmer3c
"A linear least squares problem arising from chemical kinetics."
function palmer3c(args...; kwargs...)
nlp = Model()
@variable(nlp, x[j = 1:8], start = 1.0)
X = [
-1.658063,
-1.570796,
-1.396263,
-1.221730,
-1.047198,
-0.872665,
-0.766531,
-0.698132,
-0.523599,
-0.349066,
-0.174533,
0.0,
0.174533,
0.349066,
0.523599,
0.698132,
0.766531,
0.872665,
1.047198,
1.221730,
1.396263,
1.570796,
1.658063,
]
Y = [
64.87939,
50.46046,
28.2034,
13.4575,
4.6547,
0.59447,
0.0000,
0.2177,
2.3029,
5.5191,
8.5519,
9.8919,
8.5519,
5.5191,
2.3029,
0.2177,
0.0000,
0.59447,
4.6547,
13.4575,
28.2034,
50.46046,
64.87939,
]
@NLobjective(
nlp,
Min,
0.5 * sum((Y[i] - sum(x[j] * X[i]^(2 * j - 2) for j = 1:8))^2 for i = 1:23)
)
return nlp
end