Convex or convexity may refer to:
Science and technology
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Convex lens, in optics
Mathematics
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Convex set
In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset contains the whole line segment that joins them. Equivalently, a convex set or a convex ...
, containing the whole line segment that joins points
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Convex polygon, a polygon which encloses a convex set of points
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Convex polytope
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the n-dimensional Euclidean space \mathbb^n. Most texts. use the term "polytope" for a bounded convex polytope, and the w ...
, a polytope with a convex set of points
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Convex metric space, a generalization of the convexity notion in abstract metric spaces
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Convex function
In mathematics, a real-valued function is called convex if the line segment between any two points on the graph of the function lies above the graph between the two points. Equivalently, a function is convex if its epigraph (the set of poi ...
, when the line segment between any two points on the graph of the function lies above or on the graph
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Convex conjugate, of a function
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Convexity (algebraic geometry), a restrictive technical condition for
algebraic varieties originally introduced to analyze Kontsevich
moduli spaces
Economics and finance
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Convexity (finance), second derivatives in financial modeling generally
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Convexity in economics
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Bond convexity
In finance, bond convexity is a measure of the non-linear relationship of bond prices to changes in interest rates, the second derivative of the price of the bond with respect to interest rates ( duration is the first derivative). In general, th ...
, a measure of the sensitivity of the duration of a bond to changes in interest rates
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Convex preferences In economics, convex preferences are an individual's ordering of various outcomes, typically with regard to the amounts of various goods consumed, with the property that, roughly speaking, "averages are better than the extremes". The concept roughly ...
, an individual's ordering of various outcomes
Other uses
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Convex Computer
Convex Computer Corporation was a company that developed, manufactured and marketed vector minisupercomputers and supercomputers for small-to-medium-sized businesses. Their later Exemplar series of parallel computing machines were based on the ...
, a former company that produced supercomputers
See also
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List of convexity topics
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Non-convexity (economics)
In economics, non-convexity refers to violations of the convexity assumptions of elementary economics. Basic economics textbooks concentrate on consumers with convex preferences (that do not prefer extremes to in-between values) and convex budge ...
, violations of the convexity assumptions of elementary economics
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Obtuse angle
In Euclidean geometry, an angle is the figure formed by two rays, called the '' sides'' of the angle, sharing a common endpoint, called the ''vertex'' of the angle.
Angles formed by two rays lie in the plane that contains the rays. Angles ...
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