konveksne

Konveksne is the feminine plural form of the adjective konveksan in several South Slavic languages, including Croatian, Serbian, Bosnian and Slovenian. It describes objects, shapes or concepts that exhibit convexity. In mathematical discourse, konveksne is used in phrases such as konveksne figure, konveksne funkcije and konveksne površine to denote convex versions of generic nouns.

Origin and usage: The word derives from the Latin convexus. In Slavic languages it arrived through contact with Latin and later through German or French loanwords, acquiring standard forms such as konveksan/konveksno.

Mathematics: A set S is convex if, for any two points x and y in S, the line segment connecting x and y lies entirely in S. A function f is convex if its epigraph is convex or, equivalently, if f(tx+(1−t)y) ≤ t f(x) + (1−t) f(y) for all t in [0,1]. The convex hull of a set is the smallest convex set containing it.

Applications: The concept is central in geometry, optimization, computer graphics and computational geometry, where convexity informs algorithms and analysis in areas such as linear programming, shape modeling and market theory.

See also: concave, convex hull, convex optimization.