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Convex and Concave is a lithograph print by the Dutch artist M. C. Escher, first printed in March 1955. It depicts an ornate architectural structure with...

while a concave function's graph is shaped like a cap ∩ {\displaystyle \cap } . A twice-differentiable function of a single variable is convex if and only...

mathematics, a concave function is one for which the value at any convex combination of elements in the domain is greater than or equal to the convex combination...

with a curved reflecting surface. The surface may be either convex (bulging outward) or concave (recessed inward). Most curved mirrors have surfaces that...

non-convex sets. A set that is not convex is called a non-convex set. A polygon that is not a convex polygon is sometimes called a concave polygon, and some...

A simple polygon that is not convex is called concave, non-convex or reentrant. A concave polygon will always have at least one reflex interior angle—that...

boundary of the polygon does not cross itself. All convex polygons are simple. Concave: Non-convex and simple. There is at least one interior angle greater...

over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms...

of the other surface. A lens with one convex and one concave side is convex-concave or meniscus. Convex-concave lenses are most commonly used in corrective...

In convex analysis, a non-negative function f : Rn → R+ is logarithmically concave (or log-concave for short) if its domain is a convex set, and if it...

quasiconvex function that is neither convex nor continuous. Convex function Concave function Logarithmically concave function Pseudoconvexity in the sense...

mirror Concave function, the negative of a convex function Concave polygon, a polygon which is not convex Concave set The concavity of a function, determined...

very similar to convex and concave functions. For this reason, an optimization problem which concerns optimizing a convex or concave function can also...

and angles are equal. It is possible to go past these limiting cases, creating concave or nonconvex pyritohedra. The endo-dodecahedron is concave and...

or crossed). Simple quadrilaterals are either convex or concave. The interior angles of a simple (and planar) quadrilateral ABCD add up to 360 degrees...

In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined...

mixture of convex and concave circular arc edges. Three given angles θ 1 {\displaystyle \theta _{1}} , θ 2 {\displaystyle \theta _{2}} , and θ 3 {\displaystyle...

Schur, Schur-convex functions are used in the study of majorization. A function f is 'Schur-concave' if its negative, −f, is Schur-convex. Every function...

either convex (bending outward) or concave (bending inward). The intersection of three disks forms a circular triangle whose sides are all convex. An example...

constructed from the centers and crossing points of any two intersecting circles. Kites as described here may be either convex or concave, although some sources...