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Looking at the second derivative
- 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.
math.stackexchange.com/questions/4464576/how-to-check-the-convexity-of-a-functionconvex analysis - How to check the convexity of a function ...
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Can a function with a non negative second derivative be 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 $f''(x) \geq 0 \quad \forall x \in I$.
- 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
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 ...
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.
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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: $$f(x_1,x_2)= \max\{x_1^6,e^{x_1+3x_2^2},3x_1^2-x_1x_2+x_2^4-\log(x_2+2)\}$$ With $x_2>-2...
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In this explainer, we will learn how to determine the convexity of a function as well as its inflection points using its second derivative. Before you start with this explainer, you should be confident finding the first and second derivatives of functions using the standard rules for differentiation.
