convexproof

2016年3月1日—Lemma1.Strongconvexity⇒Strictconvexity⇒Convexity.(Buttheconverseofneitherimplicationistrue.)Proof:Thefactthatstrict ...,Proposition:Afunctionf:Rn→Risconvexifandonlyifepif⊂Rn+1isconvex.Proof.Assumefisconvex.Let(x1,t1),(x2,t2)∈epifandλ∈[0,1] ...,2021年9月5日—Theorem4.6.1...LetIbeanintervalofR.Afunctionf:I→Risconvexifandonlyifforeveryλi≥0,i=1,…,n,with∑ni=1λi=1(n≥2)andfor ...,Inprobab...

參考資訊如下
1 Theory of convex functions

2016年3月1日 — Lemma 1. Strong convexity ⇒ Strict convexity ⇒ Convexity. (But the converse of neither implication is true.) Proof: The fact that strict ...

1.3 Convex Functions

Proposition: A function f : Rn → R is convex if and only if epif ⊂ Rn+1 is convex. Proof. Assume f is convex. Let (x1,t1), (x2,t2) ∈ epif and λ ∈ [0, 1] ...

4.6

2021年9月5日 — Theorem 4.6.1 ... Let I be an interval of R. A function f:I→R is convex if and only if for every λi≥0,i=1,…,n, with ∑ni=1λi=1 (n≥2) and for ...

Convex function

In probability theory, a convex function applied to the expected value of a random variable is always bounded above by the expected value of the convex function ...

Convexity

2.1 That's great, but how do I prove that a function is convex? 1. If you know calculus, take the second derivative. It is a well-known fact that if the second ...

Convexity Examples 1 Convex Functions

To prove convexity, you need an argument that allows for all possible values of x1, x2, and λ, whereas to disprove it you only need to give one set of values.

How to check if a function is convex

2019年8月16日 — What you gave is the standard definition of a convex function. If f is supposed to be continuous, it is enough to check that.

Prove $f(x,y)= x^2 + y^2$ is convex function

2022年8月2日 — Consider that f(x)=x2 has f″(x)=2>0, so f is a convex function. It is also strongly convex too (and hence strictly convex) with strong convexity ...

Proving the Convexity of a Function.