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Aug 16, 2019 · For particular functions, there are indeed easier ways of checking. For example, for any function g(x) g (x) which is twice differentiable in an interval (a, b) (a, b) (∀x ∈ (a, b)(d2g d x2 ≤ 0)) g(x) is convex in (a, b) (∀ x ∈ (a, b) (d 2 g d x 2 ≤ 0)) g (x) is convex in (a, b) That is, a function with non- negative second ...
- Proper way to check convexity or concavity for a function
I am working with a function I would like to check if it is...
- Proper way to check convexity or concavity for a function
The book "Convex Optimization" by Boyd, available free online here, describes methods to check. The standard definition is if f(θx + (1 − θ)y) ≤ θf(x) + (1 − θ)f(y) for 0≤θ≤1 and the domain of x,y is also convex.
Jun 3, 2022 · With functions of one variable, you would check for convexity by looking at the second derivative. Suppose you have f(x): the function is convex on an interval I if and only if f ″ (x) ≥ 0 ∀x ∈ I.
Jan 23, 2009 · The polygon is convex if the z-components of the cross products are either all positive or all negative. Otherwise the polygon is nonconvex. If there are N points, make sure you calculate N cross products, e.g. be sure to use the triplets (p [N-2],p [N-1],p [0]) and (p [N-1],p [0],p [1]).
Dec 6, 2018 · I am working with a function I would like to check if it is convex or concave. The function is the next: f(x1,x2) = max{x61,ex1+3x22, 3x21 −x1x2 +x42 − log (x2 + 2)} f (x 1, x 2) = max {x 1 6, e x 1 + 3 x 2 2, 3 x 1 2 − x 1 x 2 + x 2 4 − log (x 2 + 2)} With x2> −2 x 2> − 2.
It is also possible to characterize concavity or convexity of functions in terms of the convexity of particular sets. Given the graph of a function, the hypograph of f, written hypf, is the set of points that lies on or below the graph of f, while the epigraph of f, written epif, is the set of points that lies on or above the graph of f.2 Formally,
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If f(x) is convex, then g(x) = f(ax+b) is also convex for any constants a; b 2 R. But the interval of convexity will change: for example, if f(x) were convex on 0 < x < 1 and we had a = 5; b = 2, then g(x) would be convex on 2 < x < 7. If f(x) and g(x) are convex, then their sum h(x) = f(x) + g(x) is convex. 5.
