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Is a concave function a quasiconvex function?
What is a quasiconvex function?
Is 0 1 A quasiconcave function?
Are quasiconcave and quasiconvex functions Compa-Rable with concave functions in theorem 29?
What is the difference between convex and quasiconvexity?
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A function $f(x)$ is said to be quasi-concave if its domain and all its $\alpha$-superlevel sets defined as $$\mathcal{S}_\alpha \triangleq\{x|x\in dom f, f(x)\geq\alpha\}$$ are convex for every $\alpha$. Another representation of quasi-concave functions: $f(x)$ is called quasi- concave if and only if
- How to determine whether a function is concave, convex, quasi ...
We say that f is concave if for all x, y ∈ Rn and for all λ...
- How to determine whether a function is concave, convex, quasi ...
A function f : S ⊂ Rn → R defined on a convex set S is concave if for any two points x1 x2 ∈ , S and for any λ ∈ [0, 1] we have: λx1 (1 − λ) x2 ≥ λf(x1) (1 − λ)f(x2) + +. is called strictly concave if for any two points x1 , x2 ∈ S and for any λ ∈ (0, 1) we have: λx1 (1 − λ) x2 > λf(x1) (1 − λ)f(x2) + +.
In mathematics, a quasiconvex function is a real -valued function defined on an interval or on a convex subset of a real vector space such that the inverse image of any set of the form is a convex set. For a function of a single variable, along any stretch of the curve the highest point is one of the endpoints.
A weaker condition to describe a function is quasiconvexity (or quasiconcav-ity). Functions which are quasiconvex maintain this quality under monotonic transformations; moreover, every monotonic transformation of a concave func-tion is quasiconcave (although it is not true that every quasiconcave function can be written as a monotonic ...
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Sep 5, 2015 · We say that f is concave if for all x, y ∈ Rn and for all λ ∈ [0, 1] we have f(λx + (1 − λ)y) ≥ λf(x) + (1 − λ)f(y). And a function is convex if − f is concave, or f(λx + (1 − λ)y) ≤ λf(x) + (1 − λ)f(y). Definition (Quasi-concave/Quasi-convex). Let f: Rn → R.
convex function is quasiconvex. Every c. Prove that the following statements are equivalent. The function f : C R is quasiconvex. →. (b) For all α R, the sublevel set x C : f(x) α is convex. ∈ { ∈ ⩽ } 7–2. (c) For all α R, the strict sublevel set x C : f(x) < α is convex. ∈ { ∈ }
If φ is concave (convex) and weakly increasing on R and f is a concave (convex) function, then φ f is concave (convex). The pointwise limit of a sequence of concave (convex) functions is concave (convex). The infimum (supremum) of a sequence of concave (convex) func-tions is concave (convex). Proof.
