[mlevental]

I don't understand? It's a piecewise differentiable function and you maximize how you maximize any such function: do gradient ascent where it's differentiable and compare against values at the boundary points (ie start, end of interval and points at which there's a removable discontinuity).

[chillee]

I don't disagree that a gradient exists. As the other commenter commented, the gradient/subgradient will usually exist.

What I'm arguing is that this gradient will not allow you to optimize anything of interest for the vast majority of programs.

[alexmlamb]

Yeah sometimes this is called a "subgradient".