What is Pseudoconcave?
pseudoconcave (not comparable) (mathematics) (said of a function) differentiable and decreasing in any direction where it has a negative directional derivative.
Is x1x2 convex?
It is not quasiconcave or concave. 1/x2 on R × R++. [ 1 −x1/x2 ] ≽ 0. Therefore, f is convex and quasiconvex.
How do you prove a function is Convexous?
A function f : Rn → R is convex if and only if the function g : R → R given by g(t) = f(x + ty) is convex (as a univariate function) for all x in domain of f and all y ∈ Rn. (The domain of g here is all t for which x + ty is in the domain of f.)
What is the meaning of convex function?
In mathematics, a real-valued function is called convex if the line segment between any two points on the graph of the function does not lie below the graph between the two points. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set.
Is exponential function convex?
The exponential function f(x)=ex is convex. It is also strictly convex, since f″(x)=ex>0, but it is not strongly convex since the second derivative can be arbitrarily close to zero. More generally, the function g(x)=ef(x) is logarithmically convex if f is a convex function.
Is convex function continuous?
If f is a convex function defined on an open interval (a, b), then f is continuous on (a, b).
Is difference of convex functions convex?
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What is a non-convex function?
A function is non-convex if the function is not a convex function. A function, g is concave if −g is a convex function. A function is non-concave if the function is not a concave function.
Is convex function differentiable?
Every convex function on I is differentiable except possibly at a countable set. When f is differentiable, Theorem 1.3 asserts that f is increasing. The converse is also true.
What is quasiconcave and quasiconvex?
The notion of quasiconcavity is weaker than the notion of concavity, in the sense that every concave function is quasiconcave. Similarly, every convex function is quasiconvex. A concave function is quasiconcave. A convex function is quasiconvex.
What is quasi concave and quasi convex?
A (strictly) quasiconvex function has (strictly) convex lower contour sets, while a (strictly) quasiconcave function has (strictly) convex upper contour sets. A function that is both quasiconvex and quasiconcave is quasilinear.