Algorithm 19.1: augmented Lagrangian algorithm. More...

Functions
function	augmentedLagrangian (in problem, in x0, in lambda0, in eps, in maxiter)
	Applies the augmented Lagrangian method to solve $\min_x f(x)$ subject to $h(x)=0,$ where $f:\mathbb{R}^n \to \mathbb{R}$ and $h:\mathbb{R}^n \to \mathbb{R}^m$ . More...

Detailed Description

Algorithm 19.1: augmented Lagrangian algorithm.

Implementation of algorithm 19.1 of [1]

Function Documentation

function augmentedLagrangian	(	in	problem,
		in	x0,
		in	lambda0,
		in	eps,
		in	maxiter
	)

Applies the augmented Lagrangian method to solve

$\min_x f(x)$

subject to

$h(x)=0,$

where $f:\mathbb{R}^n \to \mathbb{R}$ and $h:\mathbb{R}^n \to \mathbb{R}^m$ .

Parameters

problem	the name of the Octave function defining f(x), h(x) and their derivatives. The funtion has two arguments: x and index. If index=0, the objective function and its derivatives are evaluated. If index= , the constraint and its derivtives are evaluated.
x0	starting primal point (nx1)
lambda0	starting dual point (mx1)
eps	algorithm stops if $\\|\nabla L(x_k,\lambda_k\\| \leq \varepsilon$ and $\\|h(x_k)\\|^2$ .
maxiter	maximum number of iterations (default: 100)