convex function


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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 ?
For the case of neglecting the valve effects, the cost function is approximately represented as a second order equation called convex function but for the case of considering the valve effects, the cost function is approximately represented a nonconvex function, which is a sum of a convex function and a sinusoidal function similar to (1).
Let f : I [right arrow] R be a convex function defined on the interval I of real numbers and a,b [member of] I with a < b.
The concepts of convex function and subgradient are expanded from the real field to the complex field.
The main purpose from here on is to demonstrate that the game induced by a convex/concave function is equivalent to the game induced by a concave/ convex function.
It is an explicit rational, strictly convex function for all x such that [L.
n] [right arrow] R is a continuously differentiable convex function.
1] [right arrow] R U {+[infinity]} is a proper convex function.
Though (16) does not satisfy the condition of a convex optimization in which the left side of a less inequality should be a convex function, it can not prevent us from finding the minimum value of t ([t.
Considering the problem of the validity of the Euler-Lagrange equation from a different point of view, in [1], the authors introduced a method to avoid the assumption of differentiability of the convex function L to establish the validity of the Euler-Lagrange equation.
However, since the energy characteristics of the HVAC systems can be adequately approximated as a convex function (Ann et al.
2001, Inequalities for generalize weighted mean values of convex function, Math.