# steep_descent: Steepest Descent Minimization

### 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.

`fletcher_powell`

### 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 ```

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