这一节介绍了β-smooth和α-strongly convex的两个概念,这两个概念对于后续推导优化算法的收敛速度具有重要的作用。 1 Smoothness的定义 这里介绍β-smooth的概念。 如果一个函数f被称为β-smooth的,那么它的梯度是以参数β具有lipschitz连续性的 也就是说,如果f是β-smooth的,那么有:||∇f(x)−∇f(y)...
The article deals with some approaches to solving convex problems of the min-min type with smoothness and strong convexity in only one of the two groups of variables. It is shown that the proposed approaches based on Vaidya's method, the fast gradient method, and the accelerated gradient ...
44 国际基础科学大会-Euler’s constant and exponential motives-Javier Fresán 1:02:20 国际基础科学大会-Partial Differential Equations and Convexity-Benjamin Weinkove 56:16 国际基础科学大会-Future Circular Collider: Physics Case-Christophe Grojean 1:05:49 国际基础科学大会-Optimization, the Philosophical ...
1) K-strong smoothness K强光滑性1. We introduced the K-strong convexity (K-strong smoothness) in locally convex spaces, which are generalizations of both K-strong convexity (K-strong smoothness) in Banach spaces and strong convexity (K-strong smoothness) in locally convex spaces. 首先引进了...
4) K-very convexity K-很光滑5) very smoothners 很光滑 例句>> 6) extreme smoothness 很极光滑 1. The relations among the extreme smoothness and the uniform extreme smoothness of Banach spaces and average uniform convex Banach spaces were given. 给出了 Banach 空间的很极光滑性、一致极...
摘要: In this paper, smoothness and strong smoothness of vector-valued sequence spaces ss(E) equipped with sequential norms are discussed, and their criteria are given.关键词: Vector-valued sequence space smoothness strong smoothness DOI: 10.1080/02533839.2006.9671161 被引量: 5 ...
摘要: In this paper,we obtain: that ω strong (ω very) convexity and ω strong (ω very) smoothness are dual each other,a new characteristic for X to be strongly convex (very convex,strongly smooth,very smooth),a new characteristic for X to be reflexive.关键词:...
[ 11 ]. the functionals g and j defined in ( 2.22 ) are well-defined due to assumption 2 . assumption 2 ( i ) guarantees the convexity of j . from ( 2.17 ), we have that for all \(m>0\) , there is a constant \(k_m>0\) such that for all \(y_1,y_2\in l^\infty ...
For mean field games with local coupling, existence results are typically for weak solutions rather than strong solutions. We identify conditions on the Hamiltonian and the coupling, which allow us to prove the existence of small, locally unique, strong solutions over any finite time interval in ...
The smoothness and the average uniform convexity of Banach spaces; Banach空间的平均一致凸性与光滑性 更多例句>> 4) average projection 平均凸起量5) average intensity 平均光强 1. Average intensity and short-term beam spread of a laser beam propagating in a slant-path atmosphere; 斜程大气传输...