fminsearch: Derivative-free Nonlinear Function Minimization

In pracma: Practical Numerical Math Functions

Derivative-free Nonlinear Function Minimization

Description

Find minimum of multivariable functions using derivative-free methods.

Usage

fminsearch(fn, x0, ..., lower = NULL, upper = NULL,
           method = c("Nelder-Mead", "Hooke-Jeeves"),
           minimize = TRUE, maxiter = 1000, tol = 1e-08)

Arguments

fn	function whose minimum or maximum is to be found.
x0	point considered near to the optimum.
...	additional variables to be passed to the function.
lower, upper	lower and upper bounds constraints.
method	"Nelder-Mead" (default) or "Hooke-Jeeves"; can be abbreviated.
minimize	logical; shall a minimum or a maximum be found.
maxiter	maximal number of iterations
tol	relative tolerance.

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 searches for a maximum, by default for a (local) minimum.

As methods/solvers "Nelder-Mead" and "Hooke-Jeeves" are available. Only Hooke-Jeeves can handle bounds constraints. For nonlinear constraints see fmincon, and for methods using gradients see fminunc.

Important: fminsearch may only give local solutions.

Value

List with

xopt	location of the location of minimum resp. maximum.
fmin	function value at the optimum.
count	number of function calls.
convergence	info about convergence: not used at the moment.
info	special information from the solver.

Note

fminsearch mimics the Matlab function of the same name.

References

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

See Also

nelder_mead, hooke_jeeves

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), method="Nelder-Mead")
## $xmin                   $fmin
## [1] 1.414292 2.000231   [1] 1.478036e-08

fminsearch(rosena, c(-1.2, 1), a = sqrt(2), method="Hooke-Jeeves")
## $xmin                   $fmin
## [1] 1.414215 2.000004   [1] 1.79078e-12

pracma documentation built on Nov. 10, 2023, 1:14 a.m.