In this chapter, we (a) present epigraph characterization of cone-convexity, (b) introduce cone-monotonicity, and describe differential criteria of cone-convexity and cone-monotonicity, (c) present instructive examples of cone-convex and cone-monotone functions, (d) outline basic operations preserving cone-convexity and cone-monotonicity. Taken together, (b)--(d) provide simple and powerful tools allowing one to detect and utilize cone-convexity and cone-monotonicity.
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