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Aug 16, 2019 · What you gave is the standard definition of a convex function. If $f$ is supposed to be continuous, it is enough to check that $$f\left(\frac{x+y}{2}\right) \le \frac{f(x)+f(y)}{2}$$ for all $x,y$. If $f$ is twice differentiable, it is enough to check that the second derivative is non negative.
- How to check convexity? - Mathematics Stack Exchange
The book "Convex Optimization" by Boyd, available free...
- Proper way to check convexity or concavity for a function
I am working with a function I would like to check if it is...
- How to check convexity? - Mathematics Stack Exchange
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.
I read this in wikipedia that a practical test for convexity is - to check whether the 2nd derivative (Hessian matrix) of a continuous differentiable function in the interior of the convex set is non-negative (positive semi-definite). So how to check for the convexity of functions like f(x) = |x| f (x) = | x | which is differentiable at all ...
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.
Answer. Exercise \PageIndex {4} Prove that each of the following functions is convex on the given domain: f (x)=e^ {b x}, x \in \mathbb {R}, where b is a constant. f (x)=x^ {k}, x \in [0, \infty) and k \geq 1 is a constant. f (x)=-\ln (1-x), x \in (-\infty, 1).
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This video teaches us what a convex set is and how to find out the convexity and concavity of a function using derivatives and the HESSIAN matrix.Thank you.
- 13 min
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- Reindolf Boadu
