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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
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. All convex combinations are within the convex hull of the given points.
The test functions used to evaluate the algorithms for MOP were taken from Deb, [4] Binh et al. [5] and Binh. [6] The software developed by Deb can be downloaded, [ 7 ] which implements the NSGA-II procedure with GAs, or the program posted on Internet, [ 8 ] which implements the NSGA-II procedure with ES.
p-adic function: a function whose domain is p-adic. Linear function; also affine function. Convex function: line segment between any two points on the graph lies above the graph. Also concave function. Arithmetic function: A function from the positive integers into the complex numbers. Analytic function: Can be defined locally by a convergent ...
Periodic function; List of periodic functions; Pfaffian function; Piecewise linear function; Piecewise property; Polyconvex function; Positive-definite function; Positive-real function; Progressive function; Proper convex function; Proto-value function; Pseudoanalytic function; Pseudoconvex function
Pages in category "Convex geometry" The following 54 pages are in this category, out of 54 total. ... Strictly convex set; Support function; Supporting hyperplane;
A convex curve (black) forms a connected subset of the boundary of a convex set (blue), and has a supporting line (red) through each of its points. A parabola, a convex curve that is the graph of the convex function () = In geometry, a convex curve is a plane curve that has a supporting line through each of its points.
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.