# steep_descent: Steepest Descent Minimization In pracma: Practical Numerical Math Functions

## Description

Function minimization by steepest descent.

## Usage

 1 2 steep_descent(x0, f, g = NULL, info = FALSE, maxiter = 100, tol = .Machine\$double.eps^(1/2))

## Arguments

 x0 start value. f function to be minimized. g gradient function of f; if NULL, a numerical gradient will be calculated. info logical; shall information be printed on every iteration? maxiter max. number of iterations. tol relative tolerance, to be used as stopping rule.

## Details

Steepest descent is a line search method that moves along the downhill direction.

## Value

List with following components:

 xmin minimum solution found. fmin value of f at minimum. niter number of iterations performed.

## Note

Used some Matlab code as described in the book “Applied Numerical Analysis Using Matlab” by L. V.Fausett.

## References

Nocedal, J., and S. J. Wright (2006). Numerical Optimization. Second Edition, Springer-Verlag, New York, pp. 22 ff.

## Examples

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ## Rosenbrock function: The flat valley of the Rosenbruck function makes ## it infeasible for a steepest descent approach. # rosenbrock <- function(x) { # n <- length(x) # x1 <- x[2:n] # x2 <- x[1:(n-1)] # sum(100*(x1-x2^2)^2 + (1-x2)^2) # } # steep_descent(c(1, 1), rosenbrock) # Warning message: # In steep_descent(c(0, 0), rosenbrock) : # Maximum number of iterations reached -- not converged. ## Sphere function sph <- function(x) sum(x^2) steep_descent(rep(1, 10), sph) # \$xmin 0 0 0 0 0 0 0 0 0 0 # \$fmin 0 # \$niter 2

### Example output

\$xmin
[1] 0 0 0 0 0 0 0 0 0 0

\$fmin
[1] 0

\$niter
[1] 2

pracma documentation built on Dec. 11, 2021, 9:57 a.m.