dfp {Bhat}

Function minimization with box-constraints

Description

This Davidon-Fletcher-Powell optimization algorithm has been ‘hand-tuned’ for minimal setup configuration and for efficency. It uses an internal logit-type transformation based on the pre-specified box-constraints. Therefore, it usually does not require rescaling (see help for the R optim function). dfp automatically computes step sizes for each parameter to operate with sufficient sensitivity in the functional output. Performance is comparable to the BFGS algorithm in the R function optim. dfp interfaces with newton to ascertain convergence, compute the eigenvalues of the Hessian, and provide 95% confidence intervals when the function to be minimized is a negative log-likelihood.

Usage

dfp(x, f, tol = 1e-05, nfcn = 0, ...)

Arguments

x

a list with components 'label' (of mode character), 'est' (the parameter vector with the initial guess), 'low' (vector with lower bounds), and 'upp' (vector with upper bounds)

f

the function that is to be minimized over the parameter vector defined by the list x

tol

a tolerance used to determine when convergence should be indicated

nfcn

number of function calls

...

other parameters to be passed to 'f'

Details

The dfp function minimizes a function f over the parameters specified in the input list x. The algorithm is based on Fletcher's "Switching Method" (Comp.J. 13,317 (1970))

the code has been 'transcribed' from Fortran source code into R

Value

list with the following components:

fmin

the function value f at the minimum

label

the labels taken from list x

est

a vector of the estimates at the minimum. dfp does not overwrite x

status

0 indicates convergence, 1 indicates non-convergence

nfcn

no. of function calls

Note

This function is part of the Bhat exploration tool

Author(s)

E. Georg Luebeck (FHCRC)

References

Fletcher's Switching Method (Comp.J. 13,317, 1970)

See Also

optim, newton, ftrf, btrf, logit.hessian

Examples

        # generate some Poisson counts on the fly
          dose <- c(rep(0,50),rep(1,50),rep(5,50),rep(10,50))
          data <- cbind(dose,rpois(200,20*(1+dose*.5*(1-dose*0.05))))

        # neg. log-likelihood of Poisson model with 'linear-quadratic' mean: 
          lkh <- function (x) { 
          ds <- data[, 1]
          y  <- data[, 2]
          g <- x[1] * (1 + ds * x[2] * (1 - x[3] * ds)) 
          return(sum(g - y * log(g)))
          }

	# for example define
          x <- list(label=c("a","b","c"),est=c(10.,10.,.01),low=c(0,0,0),upp=c(100,20,.1))

	# call:
	  results <- dfp(x,f=lkh)