Optimization: principles and algorithms, by Michel Bierlaire
Functions
augmentedLagrangian.m File Reference

Algorithm 19.1: augmented Lagrangian algorithm. More...

Go to the source code of this file.

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]

Note
Tested with run1905.m
Tested with run1906.m
Author
Michel Bierlaire
Date
Mon Mar 23 15:45:36 2015

Definition in file augmentedLagrangian.m.

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
problemthe 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 $f$ and its derivatives are evaluated. If index= $i$, the constraint $h_i$ and its derivtives are evaluated.
x0starting primal point (nx1)
lambda0starting dual point (mx1)
epsalgorithm stops if $\|\nabla L(x_k,\lambda_k\| \leq \varepsilon $ and $\|h(x_k)\|^2$.
maxitermaximum number of iterations (default: 100)
Returns
[solution,lambda]
x: primal solution
lambda: dual solution
Copyright 2015-2016 Michel Bierlaire