Examples of non-differentiable problems in economics As a research project, we're investigating various algorithms developed for non-differentiable, convex (or concave, if you're into economics) optimization. I'd like to find some good examples of real problem formulations that arise in different fields, especially economics. 

Any example is welcome, as long as it is non-smooth in some sense, either in the objective function or the feasible set. Ideally I'd like examples of both strictly concave and not strictly concave functions. Both problems that are separably concave and problems that aren't are of interest.
Here are four I could think of:


Leontief and Lexicographic functions, used in preferences or
production functions are non-differentiable.
Labor models often employ a discrete labor supply (work or don't
work, sometimes alongside the decision of how much or how hard to
work).
Housing models often employ a non-convex adjustment cost to ensure
that there is a discontinuity in the cost function for the choice of
housing.
Kinked objective functions, where at one or more points the
left-hand and right-hand limits  differ, are also common in
economics (e.g. optimal option exercise at maturity)