Minimize Unconstrained Multivariable Function

Find minimum of unconstrained multivariable functions.

fminunc(x0, fn, gr = NULL, ...,
          tol = 1e-08, maxiter = 0, maxfeval = 0)

Arguments

x0: starting point.
fn: objective function to be minimized.
gr: gradient function of the objective.
...: additional parameters to be passed to the function.
tol: relative tolerance.
maxiter: maximum number of iterations.
maxfeval: maximum number of function evaluations.

Details

The method used here for unconstrained minimization is a variant of a "variable metric" resp. quasi-Newton approach.

Value

List with the following components:

par: the best minimum found.
value: function value at the minimum.
counts: number of function and gradient calls.
convergence: integer indicating the terminating situation.
message: description of the final situation.

References

J. Nocedal and S. J. Wright (2006). Numerical Optimization. Second Edition, Springer Science+Business Media, New York.

Note

fminunc mimics the Matlab function of the same name.

Author

The "variable metric" code provided by John Nash (package Rvmmin), stripped-down version by Hans W. Borchers.

Examples

  fun = function(x) 
          x[1]*exp(-(x[1]^2 + x[2]^2)) + (x[1]^2 + x[2]^2)/20
  fminunc(x0 = c(1, 2), fun)
#> $par
#> [1] -6.690718e-01 -1.165251e-10
#> 
#> $value
#> [1] -0.4052369
#> 
#> $counts
#> function gradient 
#>       30       18 
#> 
#> $convergence
#> [1] 0
#> 
#> $message
#> [1] "fminunc converged"
#> 
  ## xmin: c(-0.6691, 0.0000); fmin: -0.4052