Can you please identify what class of problem this is so that I can research algorithms for solving it please?
Its a a set of linear equations and inequalities/constraints looking like this:
a = 3*g
b = 1*h + 2
c = 1
d = 2
e = if (a >= b) then 1 else 0
f = if (a < b) then 1 else 0
g = if (c >= d) then 1 else 0
h = if (c < d) then 1 else 0
The equations can be more complicated but follow the same form e.g.
a = 3*g + 2*h + 3*i + 2
g = if (c >= d and c >= e and c >= f ) then 1 else 0
I'm not sure what you call the inequalities/constraints with if/then/else type construct and I expect there is a more standard way to express them. I think they could be expressed with the signum function but that doesn't take me much further.