subplex: Minimization of a function by the subplex algorithm

Description

subplex minimizes a function.

Usage

subplex(par, fn, control = list(), hessian = FALSE, ...)

Value

subplex returns a list containing the following:

par: Estimated parameters that minimize the function.
value: Minimized value of the function.
count: Number of function evaluations required.
convergence: Convergence code (see Details).
message: A character string giving a diagnostic message from the optimizer, or 'NULL'.
hessian: Hessian matrix.

Arguments

par

Initial guess of the parameters to be optimized over.

fn

The function to be minimized. Its first argument must be the vector of parameters to be optimized over. It should return a scalar result.

control

A list of control parameters, consisting of some or all of the following:

reltol: The relative optimization tolerance for par. This must be a positive number. The default value is .Machine$double.eps.
maxit: Maximum number of function evaluations to perform before giving up. The default value is 10000.
parscale: The scale and initial stepsizes for the components of par. This must either be a single scalar, in which case the same scale is used for all parameters, or a vector of length equal to the length of par. For parscale to be valid, it must not be too small relative to par: if par + parscale = par in any component, parscale is too small. The default value is 1.

hessian

If hessian=TRUE, the Hessian of the objective at the estimated optimum will be numerically computed.

...

Additional arguments to be passed to the function fn.

Author

Aaron A. King kingaa@umich.edu

Details

The convergence codes are as follows:

-2: invalid input
-1: number of function evaluations needed exceeds maxnfe
0: success: tolerance tol satisfied
1: limit of machine precision reached

For more details, see the source code.

References

T. Rowan, ``Functional Stability Analysis of Numerical Algorithms'', Ph.D. thesis, Department of Computer Sciences, University of Texas at Austin, 1990.

Examples

Run this code

ripple <- function (x) {
  r <- sqrt(sum(x^2))
  1-exp(-r^2)*cos(10*r)^2
}

subplex(par=c(1),fn=ripple,hessian=TRUE)

subplex(par=c(0.1,3),fn=ripple,hessian=TRUE)

subplex(par=c(0.1,3,2),fn=ripple,hessian=TRUE)
## Rosenbrock Banana function
rosen <- function (x) {
  x1 <- x[1]
  x2 <- x[2]
  100*(x2-x1*x1)^2+(1-x1)^2
}

subplex(par=c(11,-33),fn=rosen)

## Rosenbrock Banana function (using names)
rosen <- function (x, g = 0, h = 0) {
  x1 <- x['a']
  x2 <- x['b']-h
  100*(x2-x1*x1)^2+(1-x1)^2+g
}

subplex(par=c(b=11,a=-33),fn=rosen,h=22,control=list(abstol=1e-9,parscale=5),hessian=TRUE)

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