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**Convex** means *curving out* or *extending outward* (compare concave).**Convex** or **convexity** may refer to:

- Convex set, a set of points containing all line segments between each pair of its points
- Convex function, a function whose epigraph forms a convex set
- Convex polytope, a polytope that forms a convex set
- Convex hull, the minimal convex set containing a set of points X
- Convex combination, a linear combination of points with non-negative coefficients that sum up to 1
- Convex conjugate, a generalization of the Legendre transformation
- Convex bipartite graph
- Convex polygon
- Convex plane graph, a plane graph with convex faces
- Convex optimization, a subfield of optimization, studies the problem of minimizing convex functions
- Convex geometry, the branch of geometry studying convex sets, mainly in Euclidean space
- Convex curve, the boundary of a convex set
- Convex body, a compact convex set with non-empty interior

- Convexity in economics
- Convex preferences, a preference relation with convex upper contour sets

- Convexity (finance), second derivatives in financial modeling generally
- Bond convexity, a measure of the sensitivity of the duration (not price) of a bond to changes in interest rates

- Convex lens, a lens with surfaces that curve outward
- Convex Computer, a company that produced a number of vector supercomputers
- Convex Software Library, a client-side open source solution for Internet Explorer

- Non-convexity (economics), violations of the convexity assumptions of elementary economics
- Concave (disambiguation)
- List of convexity topics
- Obtuse angle
- Kachurovskii's theorem

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