steep_descent: Steepest Descent Minimization

In pracma: Practical Numerical Math Functions

Steepest Descent Minimization

Description

Function minimization by steepest descent.

Usage

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.

See Also

fletcher_powell

Examples

##  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

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