我们尝试将一个凸的quasi convex function f的sublevel set表示为凸函数的不等式集合,比如给出quasi convex function f和一系列凸函数\phi_t并且具有如下性质 f(x)\leq t\Leftrightarrow \phi_t(x)\leq 0 即f(x)的t-sublevel set是\phi_t的0 sublevel set,显然
从而f,g都是log-convex的等价于对任意α,αT∇2f(x)α≥[αT∇f(x)]2f(x),αT∇2g(x)...
log-convex functionslinear functional analysisnonlinear meanlogarithmic meangeometric mean/ A0230 Function theory, analysis A0240 Geometry, differential geometry, and topology B0220 Mathematical analysis B0250 Combinatorial mathematics C1120 Mathematical analysis C1160 Combinatorial mathematics E0210C Mathematical...
凸函数和凹函数是从国外翻译过来的，凸函数就是convex function，凹函数是concave function；但是国内有些对凹函数和凸函数的定义是符合楼主的习惯的，下面是一些比较权威网站的截图向下凸才叫凸，向下凹才叫凹。这样判断就可以：在函数图像上任选两点，连接做线段，如果这条线段在这段函数图像下方，这就是...
Cohen asserts that the spectral radius of a nonnegative matrix is a convex function of the diagonal elements. The first section of this paper gives a new, unified proof of these results and also analyzes exactly when one has strict convexity. The second section gives some very simple proofs ...
A log convex function is also convex, so ifp(aN|tN)p(aN|tN)were log convex it would also be convex which doesn't make sense since it is a probability distribution and it doesn't agree with the next statement in the book that it has a global maximum. ...
Affine invariant points and maps for sets were introduced by Grünbaum to study the symmetry structure of convex sets. We extend these notions to a functional setting. The role of symmetry of the set is now taken by evenness of the function. We show that among the examples for affine invaria...
when I run it for different Inputs, I get “Disciplined convex programming error: Illegal operation: log( {convex} )” that is because of the term inside the \log, \sqrt{\alpha}, which is a convex function. How can I reformulated the objective in a way that Disciplined...
Log-convex matrix functions 来自 ResearchGate 喜欢 0 阅读量: 52 作者:JS Aujla,MS Rawla,HL Vasudeva 摘要: The authors study log-convexity for matrix functions and consider the gamma function in this setting. They also consider the notion of log-convexity on the positive cone of positive ...
Suppose that μ is a probability measure on a space X and g : X\rightarrow I\subset \mathbb{R} is a μ-integrable function, where I is a possibly infinite interval. If \varphi :X\rightarrow I\subset \mathbb{R} is a strictly convex function, then \int _{X}\varphi \bigl(g(x...