Solving 12 Inequalities w/ Neural Networks

[ramollari]

This problem appeared while working on a neural networks practical.
There are given 12 inequalities (x_0, x_1, x_2, x_3, x_4 unknown) of the form:

$$x_0 + ax_1 + bx_2 + cx_3 + dx_4 >= 0$$

or,

$$x_0 + ax_1 + bx_2 + cx_3 + dx_4 < 0$$,

and that there exists a set of solutions that satisfy all 12 inequalities. I have to find one of those solutions but I don't know where I can start to attack this problem? I'm unable to apply trial and error, due to the high number of unknowns. I'm not finding a rigorous methodology either. Does anyone have any suggestion? Does any software package exist that aids me to do this?
Thanks a lot!

 

[Galileo]

I think there's an algorithm for this. Look for the Simplex method.

 

[PerennialII]

Yeah, linear optimization/programming methods will do it for you. For example Matlab has a nice set of tools ... at least if you have access to the optimization toolbox.

 

[Data]

Maple can solve systems of linear inequalities, though its capabilities are somewhat limited. I'll give a similar problem a try later.

 

[ramollari]

I think there's an algorithm for this. Look for the Simplex method.

I think that this is an optimization method.

 

[PerennialII]

I think that this is an optimization method.

That it is ... but the idea still applies if you proceed solving as a minimization / maximization problem using the inequalities as constraint eqs ... then number of eqs wouldn't pose a problem.