Search results
- Yes! Both linear and affine functions are both convex and concave.
faculty.fiu.edu/~boydj/mathecon/math21.pdf
People also ask
Is a concave function a quasiconvex function?
Are utility functions quasi concave?
What is the difference between convex and quasiconvexity?
Is a function concave or convex?
What is a quasiconvex function?
How do you know if a function is quasiconvex?
A function is concave (convex) if the graph of the function is always above (below) any chord (line segment between two points in the graph). Remark 4. f concave ⇔−f convex. Example 5. Let S = [0,∞) and consider f(x) = √ x and g(x) = −f(x) = − √ x f is a concave function and g is a convex function. 1.2 Selected properties of ...
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
For example, f(x) transformation, but g(f(x)) = = −x2 is concave, and g(x) 2 = ex is a monotonic e−x2. 2 is not concave. This is problematic when we want to analyze things like utility which we consider to be ordinal concepts. A weaker condition to describe a function is quasiconvexity (or quasiconcav-ity).
- 212KB
- 8
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.
KC Border Quasiconvex Functions I 7–3 7.2.4 Example Note that strict quasiconvexity implies Condition (E). The con-verse does not hold. In fact, Condition (E) alone does not guarantee even quasi-convexity. For instance, the function f: Rm → R defined by f(x) = 1 x = 0, 0 x ̸= 0 . is not quasiconvex, since the sublevel set {f < 1} = Rm \{0 ...
- 83KB
- 6
Yes! Both linear and affine functions are both convex and concave. Example 21.1.2: Convex Functions. Any linear function f(x) = p·x is both concave and convex, as is the generic affine function f(x) = a+p·x.
Definition: A function is strictly quasiconvex if all of its lower contour sets are strictly convex sets and none of its level sets have any width (i.e., no interior). The first condition rules out straight-line level sets while the second rules out flat spots.
