Minimal L1 norm solution

  • Thread starter umarkhan
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  • #1
umarkhan
8
0
Hi,
Can anyone tell me how to find the minimal L1 norm solution to the problem Ax=b using a linear programming method possibly the simplex search??

Any links where I can find something ??

Khan.
 

Answers and Replies

  • #3
umarkhan
8
0
hi,
Thanks for the link. I tried some thing similar for the system x1 + x2 = 1. I converted to linear programming problem and then used linprog from matlab. The trick is to to put the L1 norm minimization in the for of two inequalities for each variable.

f=[1 1 0 0 ]';
A=[-1 0 -1 0;
-1 0 1 0;
0 -1 0 -1;
0 -1 0 1];



b=[0 0 0 0]';

Aeq=[0 0 1 1];
beq=[1];

[x,fval,exitflag,output,lambda] =linprog(f,A,b,Aeq,beq,[0 0 -10 -10]',[1e10 1e10 10 10 ])
 

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