This chapter introduces convex and concave functions defined on convex sets in Rn and gives some of their basic properties and provides some fundamental theorems involving these functions. These theorems are ver
A linear function is both convex and concave. f(x)=|x|f(x)=|x| is a convex function. f(x)=1xf(x)=1x is a convex function.TheoremLet f1,f2,...,fk:Rn→Rf1,f2,...,fk:Rn→R be convex functions. Consider the function f(x)=∑j=1kαjfj(x)f(x)=∑j=1kαjfj(x) ...
Multiplication,addition and integration log convex function乘积是log convex function 积分,如果f(x,y)是log-convex那么对于\forall y\in C,g(x)=\int_C f(x,y)dy是log-convex的 Integration of log-concave functions log-concave在积分下不能保证log-concave的性质,但是假设f:R^n\times R^m\to R是lo...
Convexandconcavefunctions 2.5.Convex and concave functions Let f be a real-valued function f:S→R.In what follows,we assume that S⊆R n is a convex set.The function f is convex on a set S if∀x1,x2∈S,∀λ∈[0,1]such thatλx1+(1−λ)x2∈S,f(λx1+(1−λ)x2)≤...
Concave and Convex Function 技术标签:函数mathConcaveConvexmachine-learning 查看原文 多载波MIMO信道下的波束成形设计 whentheweights are in increasing order ,anditisthenaSchur-concavefunctiononeach carrier...isthenaSchur-concavefunction.Theproblem inconvexform (theobjectiveislinearandthe...
1) convex and concave functions 凹凸函数 1. This article popularizes the single-dimensional random variable f≤Ef(ξ)(f(x) as convex and concave function into the multi-dimentional scope;therefore concludes a series of important inequalties esp,toconvex and concave functions. ...
Norm inequalities involving convex and concave functions of operatorsClarkson inequalitiesunitarily invariant normSchatten p-normconvex functionconcave function47A3047B1047B1546B20Let A1,…,An be bounded linear operators on a complex separable Hilbert space H and let α1,…,αn be positive real ...
The link between convex sets and convex functions is via the epigraph. A function is convex iff. its epigraph is a convex set. Similarly, a function f is concave iff. its hypograph defined as: \bold{hypo}\; f = \{(x, t) | t \le f(x)\} is a convex set....
网络凹凸函数 网络释义 1. 凹凸函数 伪凹函数,pseudoconcave... ... ) upper convex function 上凹函数 )convex and concave functions凹凸函数... www.dictall.com|基于 1 个网页
Th. Composition of convex/concave functions Assume h:R→Rh:R→R and g:RN→Rg:RN→R are twice differentiable. Define f(x)=h(g(x)),∀x∈RNf(x)=h(g(x)),∀x∈RN, thenhh is convex & non-decreasing, gg is convex ⟹⟹ ff is convex hh is convex & non-increasing, gg is...