How do you proof a function is convex? Theorem 1.What is the proof? If M(x, y) and N(x, y) are both homogeneous and of the same degree, the function \frac{M(x, y)}{N(x, y)} is homogeneous of degree Zero. Theorem 2.If f(x,...
Yes, there are other methods to prove that e^x is convex. One method is to show that the function is continuous and has a positive second derivative at every point. Another method is to use the convexity criteria, which states that if the second derivative of a function is always ...
Show how to prove a function is convex. How to prove concave and convex must be linear function? How to prove that the cubic-bezier is second-order continuous? Prove the following by using Fundamental Theorem of Algebra. Does this use Rolle's theorem? How would one prove this?
A setΩ⊂RnΩ⊂RnΩ⊂RnΩ⊂Rnis convex ifαx+(1−α)y∈Ω,∀x,y∈Ωαx+(1−α)y∈Ω,∀x,y∈Ωand∀α∈[0,1]∀α∈[0,1]. With this it should be easy enough to prove that a set is not convex: just find a counterexample. But how do you prove that iti...
Almost any ternary search task. Try to prove whether the objective function is convex before you solve it! Medium Difficulty NCNA 2019 — "Weird Flecks, but OK": Usage of the Smallest Enclosing Circle task.(Kattis)(Baekjoon) Waterloo's local Programming Contests — "A Star not a Tree?":...
Can one use Pick's theorm to prove that area size 5 covers at least 6 grid points? 0 How do you prove the arithmetic mean of vertices of a polygon lies in itself? 1 Area enclosed by a polygon 5 Determine whether a polygon is convex based on its vertices. ...
There has been a recent surge of interest in the study of asymptotic reconstruction performance in various cases of generalized linear estimation problems in the teacher-student setting, especially for the case of i.i.d standard normal matrices. Here, we go beyond these matrices, and prove an ...
Add a comment | 4 Answers Sorted by: Reset to default 2 Have you tried? (where X is 0 or 1.) struct Data_Info { unsigned char const * data_ptr; unsigned int data_size; unsigned int data_version; }; fileX.h extern const struct Data_Info data_infoX; fileX.c const stru...
How to show that a set is closed?A Closed SetIn this question we define a closed set from the area of Real Analysis in Mathematics. From the area of Real Analysis, a set is closed if it is not open or its complement is an open set. Also from the Topological perspective, a set is...
where \({\mathbb {I}}\) is the indicator function; i.e., \({\mathcal {E}}_{\mathbb {P}}(h, f)\) is the probability that h disagrees with f. If h is a hypothesis and f is a labeling function for \({\mathbb {P}}\) which we would like to approximate by h, we call ...