pracma (version 1.9.3)

fminsearch: Minimum Finding

Description

Find minimum of unconstrained multivariable function.

Usage

fminsearch(f, x0, ..., minimize = TRUE, dfree = TRUE, maxiter = 1000, tol = .Machine$double.eps^(2/3))

Arguments

f

function whose minimum or maximum is to be found.

x0

point considered near to the optimum.

minimize

logical; shall a minimum or a maximum be found.

dfree

logical; apply derivative-free optimization or not.

maxiter

maximal number of iterations

tol

relative tolerance.

...

additional variables to be passed to the function.

Value

List with

xopt

location of the location of minimum resp. maximum.

fval

function value at the optimum.

niter

number of iterations.

Details

fminsearch finds the minimum of a nonlinear scalar multivariable function, starting at an initial estimate and returning a value x that is a local minimizer of the function.

With minimize=FALSE it seaches for a maximum. dfree=TRUE applies Nelder.Mead, else Fletcher-Powell, calculating the derivatives numerically. This is generally referred to as unconstrained nonlinear optimization. fminsearch may only give local solutions.

References

Nocedal, J., and S. Wright (2006). Numerical Optimization. Second Edition, Springer-Verlag, New York.

See Also

optim

Examples

# Rosenbrock function
rosena <- function(x, a) 100*(x[2]-x[1]^2)^2 + (a-x[1])^2  # min: (a, a^2)

fminsearch(rosena, c(-1.2, 1), a = sqrt(2))
# x = (1.414214 2.000010) , fval = 1.239435e-11

fminsearch(rosena, c(-1.2, 1), dfree=FALSE, a = sqrt(2))
# x = (1.414214 2.000000) , fval = 3.844519e-26