Optimization: principles and algorithms, by Michel Bierlaire
Functions

Algorithm 17.1: projected gradient Implementation of algorithm 17.1 of [1]. More...

Go to the source code of this file.

Functions

function projectedGradient (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 17.1: projected gradient Implementation of algorithm 17.1 of [1].

Note
Tested with run1702.m
Author
Michel Bierlaire
Date
Sun Mar 22 14:47:54 2015

Definition in file projectedGradient.m.

Function Documentation

function projectedGradient ( 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