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  2. Convexity in economics - Wikipedia

    en.wikipedia.org/wiki/Convexity_in_economics

    Non‑convex sets have been incorporated in the theories of general economic equilibria, [2] of market failures, [3] and of public economics. [4] These results are described in graduate-level textbooks in microeconomics, [5] general equilibrium theory, [6] game theory, [7] mathematical economics, [8] and applied mathematics (for economists). [9]

  3. Concave function - Wikipedia

    en.wikipedia.org/wiki/Concave_function

    A function f is concave over a convex set if and only if the function −f is a convex function over the set. The sum of two concave functions is itself concave and so is the pointwise minimum of two concave functions, i.e. the set of concave functions on a given domain form a semifield.

  4. Concavification - Wikipedia

    en.wikipedia.org/wiki/Concavification

    In mathematics, concavification is the process of converting a non-concave function to a concave function. A related concept is convexification – converting a non-convex function to a convex function. It is especially important in economics and mathematical optimization. [1]

  5. Convex analysis - Wikipedia

    en.wikipedia.org/wiki/Convex_analysis

    Convex analysis includes not only the study of convex subsets of Euclidean spaces but also the study of convex functions on abstract spaces. Convex analysis is the branch of mathematics devoted to the study of properties of convex functions and convex sets , often with applications in convex minimization , a subdomain of optimization theory .

  6. Convex preferences - Wikipedia

    en.wikipedia.org/wiki/Convex_preferences

    A set of convex-shaped indifference curves displays convex preferences: Given a convex indifference curve containing the set of all bundles (of two or more goods) that are all viewed as equally desired, the set of all goods bundles that are viewed as being at least as desired as those on the indifference curve is a convex set.

  7. Second derivative - Wikipedia

    en.wikipedia.org/wiki/Second_derivative

    The second derivative of a function f can be used to determine the concavity of the graph of f. [2] A function whose second derivative is positive is said to be concave up (also referred to as convex), meaning that the tangent line near the point where it touches the function will lie below the graph of the function.

  8. Extreme point - Wikipedia

    en.wikipedia.org/wiki/Extreme_point

    In mathematics, an extreme point of a convex set in a real or complex vector space is a point in that does not lie in any open line segment joining two points of . In linear programming problems, an extreme point is also called vertex or corner point of S . {\displaystyle S.} [ 1 ]

  9. Logarithmically concave function - Wikipedia

    en.wikipedia.org/wiki/Logarithmically_concave...

    The following are among the properties of log-concave distributions: If a density is log-concave, so is its cumulative distribution function (CDF). If a multivariate density is log-concave, so is the marginal density over any subset of variables. The sum of two independent log-concave random variables is log-concave. This follows from the fact ...