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  2. Convex curve - Wikipedia

    en.wikipedia.org/wiki/Convex_curve

    A plane curve is the image of any continuous function from an interval to the Euclidean plane.Intuitively, it is a set of points that could be traced out by a moving point. More specifically, smooth curves generally at least require that the function from the interval to the plane be continuously differentiable, and in some contexts are defined to require higher derivative

  3. List of convexity topics - Wikipedia

    en.wikipedia.org/wiki/List_of_convexity_topics

    Complex convexity — extends the notion of convexity to complex numbers. Convex analysis - the branch of mathematics devoted to the study of properties of convex functions and convex sets, often with applications in convex minimization. Convex combination - a linear combination of points where all coefficients are non-negative and sum to 1 ...

  4. Jensen's inequality - Wikipedia

    en.wikipedia.org/wiki/Jensen's_inequality

    Jensen's inequality generalizes the statement that a secant line of a convex function lies above its graph. Visualizing convexity and Jensen's inequality. In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function.

  5. Convex function - Wikipedia

    en.wikipedia.org/wiki/Convex_function

    Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. In simple terms, a convex function graph is shaped like a cup (or a straight line like a linear function), while a concave function's graph is shaped like a cap .

  6. Convexity in economics - Wikipedia

    en.wikipedia.org/wiki/Convexity_in_economics

    Convexity is a geometric property with a variety of applications in economics. [1] Informally, an economic phenomenon is convex when "intermediates (or combinations) are better than extremes". For example, an economic agent with convex preferences prefers combinations of goods over having a lot of any one sort of good; this represents a kind of ...

  7. Convex geometry - Wikipedia

    en.wikipedia.org/wiki/Convex_geometry

    Convex geometry is a relatively young mathematical discipline. Although the first known contributions to convex geometry date back to antiquity and can be traced in the works of Euclid and Archimedes, it became an independent branch of mathematics at the turn of the 20th century, mainly due to the works of Hermann Brunn and Hermann Minkowski in dimensions two and three.

  8. Convex analysis - Wikipedia

    en.wikipedia.org/wiki/Convex_analysis

    then is called strictly convex. [1]Convex functions are related to convex sets. Specifically, the function is convex if and only if its epigraph. A function (in black) is convex if and only if its epigraph, which is the region above its graph (in green), is a convex set.

  9. Convex graph - Wikipedia

    en.wikipedia.org/wiki/Convex_graph

    In mathematics, a convex graph may be a convex bipartite graph; a convex plane graph; the graph of a convex function This page was last edited on 28 ...