是log-concave函数 对称正定矩阵的行列式detX的行列式是log-concave函数 对称正定矩阵的行列式detX与迹的比值:detX/trX 许多概率密度分布都是log-concave函数,例如多元高斯分布: p(x)=1(2π)n|detΣ|e−12(x−μ)TΣ(x−μ) 多元指数分布:
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....
首先，log-convex函数定义为满足[公式]或[公式]，而log-concave函数则是满足[公式]或[公式]。log-convex性是凸函数的一个特性，如果一个函数是二阶可微的，可以通过二阶判定准则判断其为log-convex。
Convex and Concave Functions - Explore the concepts of convex and concave functions, their properties, and significance in optimization. Learn how these functions are used in various applications.
Moreover, the piecewise formulation that defines several popular activation functions, prevents the computation of convex/concave relaxations as they violate the factorable function requirement. To improve the performance of relaxations of ANNs for deterministic global optimization applications, this study ...
log-concave函数与log-concave函数在乘法、正数点乘以及积分运算下保持封闭性。这意味着如果两个函数都是log-concave函数，那么它们的乘积也是log-concave函数。log-convex函数的运算封闭性也适用于乘法、正数点乘和积分运算。但需要注意的是，两个log-concave函数直接相加不一定保持log-concave性质。结论 了解...
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)≤...
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...
log-concave and log-convex functions properties of log-concave functions consequences of integration property convexity with respect to generalized inequalities 1. Introduction mathematical optimization least-squares and linear programing convex optimization example course goals and topics nonlinear optimization br...
Learn how to solve convex optimization problems. Resources include videos, examples, and documentation covering convex optimization and other topics.