Initial values
When running invGauss, the initial estimates are first computed by the function f.grovest3 and printed, then the maximum likelihood estimation proceeds. The initial values are computed by assuming tau=0 and then computing the explicit MLE fit using the Kaplan-Meier curve. Then tau is, for the time being, just set equal to mu. Although far from perfect, this should give values at least of the correct order of magnitude.
An extension of this makes it possible to get initial values for the parameters associated with the covariates, but this is not yet properly incorporated, and 0 is chosen for all. (This seems not to represent any problem, though).
Maximum likelihood
The maximum likelihood computations use the R package 'optimx', which provides a common interface for optimization functions. By default, invGauss uses the BFGS method in the optim function. Other options are available; look at the optimx package documentation for details.