R: e04dg: Unconstrained minimum, preconditioned conjugate...

e04dg {NAGFWrappers}

R Documentation

e04dg: Unconstrained minimum, preconditioned conjugate gradient algorithm, function of several variables using first derivatives (comprehensive)

Description

e04dg minimizes an unconstrained nonlinear function of several variables using a pre-conditioned, limited memory quasi-Newton conjugate gradient method. First derivatives (or an ‘acceptable’ finite difference approximation to them) are required. It is intended for use on large scale problems.

Usage

e04dg(objfun, x, optlist,
      n = nrow(x))

Arguments

objfun

function

objfun must calculate the objective function F(x) and possibly its gradient as well for a specified n element vector x.

(MODE,OBJF,OBJGRD) = objfun(mode,n,x,nstate)

x

double array

An initial estimate of the solution.

optlist

options list

Optional parameters may be listed, as shown in the following table:

Name	Type	Default
`Defaults`
`Estimated Optimal Function Value`	double
`Function Precision`	double	Default = ε^0.9
`Iteration Limit`	integer	Default = max(50, 5n)
`Iters`
`Itns`
`Linesearch Tolerance`	double	Default = 0.9
`List`		Default for e04dg = list
`Nolist`		Default for e04dg = nolist
`Maximum Step Length`	double	Default = 10^20
`Optimality Tolerance`	double	Default = ε_R^0.8
`Print Level`	integer	= 0
`Start Objective Check at Variable`	integer	Default = 1
`Stop Objective Check at Variable`	integer	Default = n
`Verify Level`	integer	Default = 0
`Verify`
`Verify Gradients`
`Verify Objective Gradients`

n

integer: default = nrow(x)

, the number of variables.

Details

R interface to the NAG Fortran routine E04DGF.

Value

`ITER`	integer The total number of iterations performed.
`OBJF`	double The value of the objective function at the final iterate.
`OBJGRD`	double array The gradient of the objective function at the final iterate (or its finite difference approximation).
`X`	double array The final estimate of the solution.
`IFAIL`	integer ifail =0 unless the function detects an error or a warning has been flagged (see the Errors section in Fortran library documentation).

Author(s)

NAG

References

http://www.nag.co.uk/numeric/FL/nagdoc_fl23/pdf/E04/e04dgf.pdf

Examples


optlist <- list()

ifail <- 0
objfun = function(mode, n, x, nstate) {
    
    objgrd <- as.matrix(mat.or.vec(2, 1))
    expx1 <- exp(x[1])
    objf <- expx1 %*% (4 %*% x[1]^2 + 2 %*% x[2]^2 + 4 %*% x[1] %*% 
        x[2] + 2 %*% x[2] + 1)
    
    if (mode == 2) {
        
        objgrd[1] <- 4 %*% expx1 %*% (2 %*% x[1] + x[2]) + objf
        
        objgrd[2] <- 2 %*% expx1 %*% (2 %*% x[2] + 2 %*% x[1] + 
            1)
        
    }
    else {
        
        objgrd <- as.matrix(mat.or.vec(2, 1))
    }
    list(MODE = as.integer(mode), OBJF = objf, OBJGRD = as.matrix(objgrd))
}

x <- matrix(c(-1, 1), nrow = 2, ncol = 1, byrow = TRUE)



e04dg(objfun, x, optlist)

[Package NAGFWrappers version 24.0 Index]