f(x,y) = \displaystyle\frac{x^2}{y} (\operatorname{dom} f=\mathbf{R} \times \mathbf{R}_{++}=\left\{(x, y) \in \mathbf{R}^{2} \mid y>0\right\}) 是一个 Quadratic-over-linear function, 它是凸的。 f(x)=(\Pi_{i=1}^n x_i)^{\frac{1}{n}},x_i>0 是凹函数,...
本节考虑可微Quasiconvex function的性质 一阶条件 Suppose f:R^n \to R is differentiable. Then f is quasiconvex if and only if dom f is convex and \forall x,y\in dom f f(y)\leq f(x)\Rightarrow \nabla f(x)^T(y-x)\leq 0 回忆凸函数的一阶条件 f(y)\geq f(x)+\nabla f(x)...
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...
问如何在gurobi模型中设置NonConvex参数ENSNMP（Simple Network Management Protocol）是一种用于管理和监控...
Let r.v. XX in convex set C⊆RNC⊆RN, and convex function ff defined over CC. Then, E[X]∈C,E[f(X)]E[X]∈C,E[f(X)] is finite, andf(E[X])≤E[f(X)]f(E[X])≤E[f(X)]Sketch of proof: extending f(∑αx)≤∑αf(x)f(∑αx)≤∑αf(x) and ∑α=1∑α=...
A function f is convex if (1) Its domain dom(f ) is a convex set in Rn and (2) For all x1, x2 ∈ dom(f ) and α∈ (0, 1) f (αx1 + (1 ? α)x2) ≤αf (x1) + (1 ? α)f (x2) Convex Optimization 2 Lecture 3 More on Convex Function Def. A function f is ...
Intuitively, recall that any point on the line between two arbitrary points of a convex function will be above that function. In more formal terms, a continuous segment (that is, a straight line) connecting two arbitrary points on the graph of the objective function will not go below the ob...
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 risk is given.DOI: 10.1016/0165-1765(86)90242-9 ...
1. 凸函数 经济学专有名词 中英对照_百度文库 ... convex: 凸convex function:凸函数convex preference: 凸偏好 ... wenku.baidu.com|基于298个网页 2. 上凸函数 上凸函数,conv... ... ) convex function 凸函数 )convex function上凸函数) convex upper-continuous mapping 上半连续凸函数 ... ...
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 Conservative Stochastic Optimization With Expectation Constraints ...