# MGH09: More, Gabrow and Hillstrom example 9 In NISTnls: Nonlinear least squares examples from NIST

## 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 North-Holland.

## 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), "try-error")) 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))) ```

NISTnls documentation built on May 29, 2017, 3:49 p.m.