  Functions that are piecewise defined are a common sight in mathematics while
convexity is a property especially desired in optimization. Suppose now a
piecewise-defined function is convex on each of its defining components - when
can we conclude that the entire function is convex? In this paper we provide
several convenient, verifiable conditions guaranteeing convexity (or the lack
thereof). Several examples are presented to illustrate our results.

Classical Analysis and ODEs;Optimization and Control