Are there efficient algorithm to split a discrete function into piecewise convex functions?

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Hi guys let's say we have a function $f(x)$ where $x$ belongs to a discrete range of values (but finite).

Are there algorithms to split $f$ as piecewise convex functions? If yes what about the hypothesis on $f$?

If it is not possible for discrete function is it possible for continuous function? (i.e. defined on a continuous set)?