Steepest descent algorithm, calculating the Cauchy point at each iteration. More...

Functions
function	steepestDescentCauchy (in obj, in x0, in eps, in maxiter)
	Applies the steepest descent algorithm to solve $\min_x f(x)$ where $f:\mathbb{R}^n\to\mathbb{R}$ . The Cauchy point is calculated at each iteration. More...

Detailed Description

Steepest descent algorithm, calculating the Cauchy point at each iteration.

Function Documentation

function steepestDescentCauchy	(	in	obj,
		in	x0,
		in	eps,
		in	maxiter
	)

Applies the steepest descent algorithm to solve $\min_x f(x)$ where $f:\mathbb{R}^n\to\mathbb{R}$ . The Cauchy point is calculated at each iteration.

Parameters

obj	the name of the Octave function defining f(x) and its derivatives
x0	the starting point
eps	algorithm stops if $\\|F(x)\\| \leq \varepsilon$ .
maxiter	maximum number of iterations (Default: 100)

Returns: [solution,iteres,niter]; solution: local minimum of the function; iteres: sequence of iterates generated by the algorithm. It contains n+2 columns. Columns 1:n contains the value of the current iterate. Column n+1 contains the value of the objective function. Column n+2 contains the value of the norm of the gradient. It contains maxiter rows, but only the first niter rows are meaningful.; niter: total number of iterations