More, Gabrow and Hillstrom example 9
Description
The MGH09
data frame has 11 rows and 2 columns giving
Format
This data frame contains the following columns:
 y

A numeric vector of response values.
 x

A numeric vector of input values.
Details
This problem was found to be difficult for some very good algorithms. There is a local minimum at (+inf, 14.07..., inf, inf) with final sum of squares 0.00102734....
See More, J. J., Garbow, B. S., and Hillstrom, K. E. (1981). Testing unconstrained optimization software. ACM Transactions on Mathematical Software. 7(1): pp. 17–41.
Source
Kowalik, J.S., and M. R. Osborne, (1978). Methods for Unconstrained Optimization Problems. New York, NY: Elsevier NorthHolland.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22  Try < function(expr) if (!inherits(val < try(expr), "tryerror")) val
plot(y ~ x, data = MGH09)
## starting values for this attempt are ridiculous
Try(fm1 < nls(y ~ b1*(x**2+x*b2) / (x**2+x*b3+b4),
data = MGH09, trace = TRUE,
start = c(b1 = 25, b2 = 39, b3 = 41.5, b4 = 39)))
Try(fm1a < nls(y ~ b1*(x**2+x*b2) / (x**2+x*b3+b4),
data = MGH09, trace = TRUE, alg = "port",
start = c(b1 = 25, b2 = 39, b3 = 41.5, b4 = 39)))
Try(fm2 < nls(y ~ b1*(x**2+x*b2) / (x**2+x*b3+b4),
data = MGH09, trace = TRUE,
start = c(b1 = 0.25, b2 = 0.39, b3 = 0.415, b4 = 0.39)))
Try(fm2a < nls(y ~ b1*(x**2+x*b2) / (x**2+x*b3+b4),
data = MGH09, trace = TRUE, alg = "port",
start = c(b1 = 0.25, b2 = 0.39, b3 = 0.415, b4 = 0.39)))
Try(fm3 < nls(y ~ cbind(x, x**2) / (x**2+x*b3+b4),
data = MGH09, trace = TRUE, algorithm = "plinear",
start = c(b3 = 41.5, b4 = 39)))
Try(fm4 < nls(y ~ cbind(x, x**2) / (x**2+x*b3+b4),
data = MGH09, trace = TRUE, algorithm = "plinear",
start = c(b3 = 0.415, b4 = 0.39)))

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