Convexly

Convexly is the adverb form of convex, used to describe actions, constructions, or statements that relate to convexity. In mathematics, convexity is a property associated with sets, functions, and paths that generalizes the idea that a line segment between two points remains inside the object. The term convexly is not widely adopted in formal writing; most authors prefer phrases such as “in a convex manner,” “in a convex way,” or simply to describe the object as convex.

In practical use, convexity is central to areas such as convex analysis, optimization, and geometry. A convex set contains every line segment between any pair of its points. A convex function lies below or on its tangent lines, and a path within a convex set can be described as staying inside the set for all intermediate points. When researchers discuss methods or constructions that preserve convexity, they typically say the process preserves convexity or is convexity-preserving rather than using convexly.

Etymology traces convex to Latin convexus, meaning arched or rounded, from con- “together” and vexus “placing, lying.” Today, convexity remains a foundational concept in fields ranging from optimization theory to computational geometry. While convexly may appear in informal or explanatory contexts to convey convexity-oriented behavior, precise language commonly relies on explicit statements about convexity rather than the adverbial form.

See also: convexity, convex set, convex function, convex combination, epigraph.