fminunc: Minimize Unconstrained Multivariable Function In pracma: Practical Numerical Math Functions

Description

Find minimum of unconstrained multivariable functions.

Usage

 1 2 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.

Note

fminunc mimics the Matlab function of the same name.

Author(s)

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

References

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

Examples

 1 2 3 4 fun = function(x) x*exp(-(x^2 + x^2)) + (x^2 + x^2)/20 fminunc(x0 = c(1, 2), fun) ## xmin: c(-0.6691, 0.0000); fmin: -0.4052

Example output

\$par
 -6.690718e-01 -1.114755e-10

\$value
 -0.4052369

\$counts