[Convex Optimization Exercise -1.1]: Convexity and Concavity (以始为终) zdr0 数学话题下的优秀答主 9 人赞同了该文章 目录 收起 Question 1: Convex, Concave, Quasi-convex, and Quasi-concave Functions Solutions for Question 1 Question 2: Perspective of a Function Solution for Question...
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:
在数学分析领域，log-concave和log-convex函数具有重要应用，尤其是在优化问题中。定义上，一个函数f(x)称为log-convex函数，当它满足对数函数对任何x > y > 0都成立的条件。这可以表示为：f(x)f(y) ≥ f(x+y)或者对数函数ln(f(x))在区间上为凸函数。同理，一个函数f(x)称为log-concave...
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 ...
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)≤...
Quasiconvex & Quasiconcave functions Differentiable Quasiconvex Function Strictly Quasiconvex Function Strongly Quasiconvex Function Pseudoconvex Function Convex Programming Problem Fritz-John Conditions Karush-Kuhn-Tucker Optimality Necessary Conditions Algorithms for Convex Problems Convex Optimization Resources Con...
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...
Concave and convex functions 来自 morebooks.de 喜欢 0 阅读量: 18 作者: Andrew Owusu-Hemeng 摘要: In recent years, convex optimization has become a computational tool of central importance in mathematics and economics, thanks to its ability to solve very large, practical mathematical problems ...
In this paper, we consider functions of the form $${\\phi(x,y)=f(x)g(y)}$$ ... A Khajavirad,NV Sahinidis - 《Journal of Global Optimization》 被引量: 54发表: 2012年 Hermite-Hadamard type inequalities for s-convex and s-concave functions via fractional integrals New identity for ...
Examples are presented and some pitfalls in optimization are discussed.关键词: concave programming control system synthesis convex programming robust control three-term control PID controllers PID design convex-concave optimization convex-concave programming frequency response data ...