convex function

(redirected from Convex functional)

convex function

[′kän‚veks ′fəŋk·shən]
(mathematics)
A function ƒ(x) is considered to be convex over the interval a,b if for any three points x1, x2, x3 such that a <>x1<>x2<>x3<>b, ƒ (x2)≤ L (x2), where L (x) is the equation of the straight line passing through the points [x1, ƒ(x1)] and [x3, ƒ(x3)].
References in periodicals archive ?
We show that in virtue of the constraints, a convex optimization procedure applied to a non convex functional produces a solution that is a global optimum, as verified using genetic algorithm (GA) to check the obtained solution.
Similarly we say the map [beta] is a nonnegative continuous convex functional on a cone P of a real Banach space E if [beta] : P [right arrow] [0,[infinity]) is continuous and
Let [gamma], [beta], [theta] be nonnegative continuous convex functionals on P and [alpha],[phi] be nonnegative continuous concave functionals on P.
Suppose that there exist positive numbers c and M, nonnegative continuous concave functionals [alpha] and [phi] on P, and nonnegative continuous convex functionals [gamma], [beta] and [theta] on P, with