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

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 . More...

Detailed Description

Algorithm 17.2: preconditioned projected gradient, or constrained Newton.

Implementation of algorithm 17.2 of [1]

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

obj	the name of the Octave function defining and $\nabla f(x)$ .
A	matrix of the constraint
b	right-hand side of the constraint
x0	starting point
eps	algorithm stops if $\\|d_k\\| \leq \varepsilon$ .
gamma	parameter > 0 (default: 1)
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