I have the following constraint inequalities and equalities:
$Ax \leq b$ $A_{eq}x = b_{eq}$
The problem is that the objective function, which I am asked to minimized, is defined as
$f=\sum\limits_{i=1}^{m}u([\sum\limits_{j=1}^{n}k_{ij}x_j]-c_{i})$
where $u(x)$ is the Heaviside step function.
Strictly speaking, this is not a linear programming problem ( although quite close!), so it can't be attacked by the standard linear programming techniques.
I'm aware that I can approximate the step function into a smooth function, but this is not the route I plan to take now.
What are the techniques that are available for this kind of problem?