Your problem can be formulated as a nonlinear programming problem in such way. Let 
$$f_j(x):= \text{piecewise}  \left(\sum_{j=1}^{j=n} a_{i,j}x_j- b_i <0,0,1 \right).
$$
Then we find 
$$ \max f(x)= \sum_{i=1}^{j=m}f_i(x) $$
under the constraint
$$\sum_{j=1}^{j=n} x_j^2 =1.
$$
This can be solved by global optimizers. I use the DirectSearch in Maple
 (See http://www.maplesoft.com/applications/view.aspx?SID=101333 .).

See an example in  an *.mw file 
from   http://rapidshare.com/files/1627770637/NP.mw .