In other words, a convex function is the pointwise supremum of the set of all affine global underestimators of it. 函数复合 考虑一般函数复合的情况:f(x) = h(g(x)) 在一元的情况下,求导可得: f^{\prime \prime}(x)=h^{\prime \prime}(g(x)) g^{\prime}(x)^{2}+h^{\prime}(g...
log convex function is convex and a nonnegative concave function is log-concave 性质 Log-convex function二次微分 g(x)=\log f(x)\\ \nabla g(x)=\frac{1}{f(x)}\nabla f(x)\\ \nabla^2 g(x)=\frac{1}{f(x)}\nabla^2 f(x)-\frac{1}{f^2(x)}\nabla f(x)\nabla f(x)^T...
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...
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...
M22M22is1200x2−400y+21200x2−400y+2(we removed line 2 and column 2). If the function is convex, these minors should be nonnegativeon the interior of the convex set. Which convex set? By definition, the domain of a convex function is a convex set. In our case when we say tha...
Both non-convex technologies and cost functions (total, ray-average and marginal) are characterized by closed form expressions. Furthermore, a local duality result is established between a local cost function and the input distance function. Finally, nonparametric goodness-of-fit tests for convexity ...
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 ...
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 ...
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 ...
A non-convex function “curves up and down.” A familiar example is the sine function (SIN(C1) in Excel), which is pictured below.The feasible region of an optimization problem is formed by the intersections of the constraints. The intersection of several convex constraints is always a convex...