enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Logarithmically convex function - Wikipedia

    en.wikipedia.org/.../Logarithmically_convex_function

    A logarithmically convex function f is a convex function since it is the composite of the increasing convex function and the function , which is by definition convex. However, being logarithmically convex is a strictly stronger property than being convex.

  3. Convex function - Wikipedia

    en.wikipedia.org/wiki/Convex_function

    A function (in black) is convex if and only if the region above its graph (in green) is a convex set. A graph of the bivariate convex function x 2 + xy + y 2. Convex vs. Not convex

  4. Logarithmically concave function - Wikipedia

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

    A log-concave function is also quasi-concave. This follows from the fact that the logarithm is monotone implying that the superlevel sets of this function are convex. [1] Every concave function that is nonnegative on its domain is log-concave. However, the reverse does not necessarily hold.

  5. Gamma function - Wikipedia

    en.wikipedia.org/wiki/Gamma_function

    The last of these statements is, essentially by definition, the same as the statement that () >, where () is the polygamma function of order 1. To prove the logarithmic convexity of the gamma function, it therefore suffices to observe that () has a series representation which, for positive real x, consists of only positive terms.

  6. Sigmoid function - Wikipedia

    en.wikipedia.org/wiki/Sigmoid_function

    A wide variety of sigmoid functions including the logistic and hyperbolic tangent functions have been used as the activation function of artificial neurons. Sigmoid curves are also common in statistics as cumulative distribution functions (which go from 0 to 1), such as the integrals of the logistic density , the normal density , and Student's ...

  7. 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.

  8. 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.

  9. Barrier function - Wikipedia

    en.wikipedia.org/wiki/Barrier_function

    A barrier function is also called an interior penalty function, as it is a penalty function that forces the solution to remain within the interior of the feasible region. The two most common types of barrier functions are inverse barrier functions and logarithmic barrier functions.