Re: minimum L1 norm

[Kai Torben Ohlhus]

Hi,

You should work on your optimization problem before applying a solver. Your problem can be transformed into an linear program, see [1] for example. 

% A small example from the website [1] solved with Octave

m = 4;

n = 3;

A = [1 2 3; 4 5 6; 7 8 9; 10 11 12];

epsi = eye(m);

A = [A epsi];

b = [1; 2; 3; 4];

c = [zeros(1, n), sum(epsi)];

[x_opt, f_min] = glpk (c, A, b); % apply linear solved

x_opt(1:3) % cut off slack variables epsilon

f_min

----------------------------

ans = 0.00000   0.00000   0.33333

f_min = 0

HTH,

Kai

[1] https://reference.wolfram.com/mathematica/tutorial/ConstrainedOptimizationLinearProgramming.html#261990371

On Fri, Apr 11, 2014 at 10:43 PM, Juan Pablo Carbajal <address@hidden> wrote:

On Fri, Apr 11, 2014 at 8:05 PM, Ether Jones <address@hidden> wrote:
> Hello.
>
> I think my question is straightforward but I'm not finding the answer I need
> in the manual.
>
> I have a set of overdetermined linear equations A*x = b + epsilon.
>
> A is an MxN matrix where M>N.  A is known.
>
> b and epsilon are Mx1 column vectors.  b is known.  epsilon is unknown.
>
> x is an Nx1 column vector.  x is unknown.
>
> I want to find the value of x that minimizes the L1 norm of epsilon.
>
> What is the recommended way to do this in Octave?
>
>

> _______________________________________________
> Help-octave mailing list
> address@hidden
> https://lists.gnu.org/mailman/listinfo/help-octave
>

Get the YALL1 package
http://yall1.blogs.rice.edu/

_______________________________________________
Help-octave mailing list
address@hidden
https://lists.gnu.org/mailman/listinfo/help-octave