Exponentially concave functions
WebMay 19, 2016 · We consider exponentially concave functions on the unit simplex. In a previous paper we showed that gradient maps of exponentially concave functions provide solutions to a Monge-Kantorovich optimal transport problem and give a better …
Exponentially concave functions
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WebIn this paper we develop a concrete and fully implementable approach to the optimization of functionally generated portfolios in stochastic portfolio theory. The main idea is to optimize over a family of rank-based portfolios parameterized by an exponentially concave … WebA function is called the exponentially general concave function f, if fis exponen-tially general convex function. De nition 2.9. A function Fis said to be exponentially general a ne convex function with respect to an arbitrary non-negative function g;if
Web1. Log-concave densities / distributions: de nitions Suppose that a density f can be written as f(x) f’(x) = exp(’(x)) = exp( ( ’(x))) where ’is concave (and ’is convex). The class of all densities f on R, or on Rd, of this form is called the class of log-concave densities, Plog … WebLecture 3 Restriction of a convex function to a line f is convex if and only if domf is convex and the function g : R → R, g(t) = f(x + tv), domg = {t x + tv ∈ dom(f)} is convex (in t) for any x ∈ domf, v ∈ Rn Checking convexity of multivariable functions …
WebA function is exponentially concave if its exponential is concave. We consider exponentially concave functions on the unit simplex. In a previous paper, we showed that gradient maps of exponentially concave functions pro-vide solutions to a … WebFeb 20, 2024 · Exponentially convex functions are used to manipulate in statistical learning, sequential prediction, and stochastic optimization (see [2, 3,17] and the references therein). It is known that x 2 K...
WebSep 1, 2024 · A real-valued function φ on an open convex domain D in R n is said to be exponentially concave if exp φ is a concave function on D. For usual practices in convex analysis, we will assume our functions to take the value − ∞ outside their domains, …
WebApr 28, 2024 · We establish some new Hermite–Hadamard-type inequalities involving fractional integral operators with the exponential kernel. Meanwhile, we present many useful estimates for these types of new Hermite–Hadamard-type inequalities via exponentially convex functions. pros and cons of dataverseWebI know that exponential of a convex function is convex, but is exponential of a concave function concave?? Surely you checked that x ↦ e − x 2 is convex or concave (it is neither). In general, composing a concave function with an exponential doesn't produce a … pros and cons of data warehousesWebSep 30, 2024 · A function is called the exponentially m -concave function f, if − f is an exponentially m -convex function. It is obvious that theses two concepts are equivalent. These equivalent formulations have been used to discuss various aspects of the exponentially convex functions. rescue puppies in californiaWebA function , where is an interval, is said to be an exponentially convex function if holds for all , and . If the inequality in is reversed, then is called exponentially concave. If , then gives inequality . For some recent citations and utilization of exponentially convex functions, one can see [5–14] and references rescue raise baby monkeyWebMar 30, 2024 · Using the definition of the exponential type convex function for k=1, we have f ( m ) \leq ( e-1 ) f (m)\Longrightarrow0\leq (e-2)f (m)\Longrightarrow f (m)\geq0 . . We discuss some connections between the class of exponential type convex functions and … pros and cons of dating a modelWebExponential growth occurs when b > 1, and y-values increase to the right. Exponential decay occurs when 0 b 1, and y-values decrease to the right. Both graphs are concave-up. When a 0, the graphs of exponential equations become concave down, and increasing x-values yield increasingly negative y-values. pros and cons of data protectionWebThe logarithm f(x) = logxis concave on the interval 0 <1, and the exponential f(x) = ex is convex everywhere. 3. f(x) is convex i f(x) is concave. 4. You can combine basic convex functions to build more complicated convex functions. If f(x) is convex, then g(x) = cf(x) … pros and cons of data warehouse