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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).


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.


Yeah sometimes this is called a "subgradient".




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