Optimization: principles and algorithms, by Michel Bierlaire
Functions

Algorithm 17.2: preconditioned projected gradient, or constrained Newton. More...

Go to the source code of this file.

Functions

function constrainedNewton (in obj, in A, in b, in x0, in eps, in gamma)
 Applies the projected gradient method to solve $\min_x f(x) $ subject to $Ax = b$. More...
 

Detailed Description

Algorithm 17.2: preconditioned projected gradient, or constrained Newton.

Implementation of algorithm 17.2 of [1]

Note
Tested with run1702constrainedNewton.m
Author
Michel Bierlaire
Date
Sun Mar 22 16:25:39 2015

Definition in file constrainedNewton.m.

Function Documentation

function constrainedNewton ( in  obj,
in  A,
in  b,
in  x0,
in  eps,
in  gamma 
)

Applies the projected gradient method to solve $\min_x f(x) $ subject to $Ax = b$.

Parameters
objthe name of the Octave function defining $f(x)$ and $\nabla f(x)$.
Amatrix of the constraint
bright-hand side of the constraint
x0starting point
epsalgorithm stops if $\|d_k\| \leq \varepsilon $.
gammaparameter > 0 (default: 1)
maxitermaximum 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
Copyright 2015-2016 Michel Bierlaire