R上的Quasiconvex functions,考虑连续函数 连续函数f:R→R如果是quasiconvex当且仅当满足下列三种条件之一 f不增 f不减 $\exists c\in dom f,s.t\ \forall t\leq c $,f is nonincreasing and \forall t\geq c,t\in dom f,f is nondecreasing ...
拟凸函数(Quasiconvex functions) 拟凸这节写的不是特别完善,挖坑以后填了。 如果一个函数的下水平集是凸的,那么就称这个函数是拟凸的。 S_{\alpha}=\{x \in \operatorname{dom} f \mid f(x) \leq \alpha\} \;\text{ convex} \Longleftrightarrow f \;\text{ quasiconvex}\\ ...
随笔分类 - 介绍凸优化与非凸优化的基本概念,常用算法,主要的研究成果及其在机器视觉,压缩感知,深度学习和信息论中的应用。 Big picture of mathematical optimization 摘要:Basic concepts, optimality conditions, different types of optimization, algorithm design techniques阅读全文 posted @2020-06-29 20:47科研民工...
Vanden Eeckaut (2004): "Non-convex Technologies and Cost Functions: Definitions, Duality and Nonparametric Tests of Convexity," Journal of Economics, 81(2), 155-192.Briec W, Kerstens K, Vanden Eeckaut P. Non-convex technologies and cost functions: definitions, duality and nonparametric tests...
Convex functions Composition with scalar functions composition of g : Rn → R and h : R → R: f (x ) = h(g (x )) f is convex if ? ? nondecreasing g convex, h convex, h ? nonincreasing g concave, h convex, h proof (for n = 1, twice di?erentiable g , h de?ned ...
..fk are convex functionsTherefore, fi(λx1+(1−λ)x2)≤λfi(x1)+(1−λ)fi(x2),∀λ∈(0,1)fi(λx1+(1−λ)x2)≤λfi(x1)+(1−λ)fi(x2),∀λ∈(0,1) and i=1,2,...,ki=1,2,...,kConsider the function f(x)f(x).Therefore...
In anonseparableproblem, at least one off-diagonal term of the matrix is nonzero. CPLEX can solve minimization problems having a convex quadratic objective function. Equivalently, it can solve maximization problems having a concave quadratic objective function. All linear objective functions satisfy this...
A nonconvex surface What if the surface is non-convex? Well as you can see throwing a marble randomly onto the surface has very few chances of hitting the global minimum. Instead, it is likely that the marble will fall into one of the many local minima. And when this is the case, wh...
On the Equivalence between Herding and Conditional Gradient Algorithms Stochastic first-order methods for convex and nonconvex functional constrained optimization Lazifying Conditional Gradient Algorithms Dose-volume histograms New Analysis and Results for the Frank-Wolfe Method ...
Convex functions on non-convex domains 来自 dx.doi.org 喜欢 0 阅读量: 78 作者:HJM Peters,PP Wakker 摘要: It is shown that a convex function, defined on an arbitrary, possibly finite, subset of a linear space, can be extended to the whole space. An application to decision making under ...