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29 октября в 115 КПМ пройдут заседания Математического кружка и Межкафедрального семинара

В 17-00 профессор Ю.Е.Нестеров прочтет лекцию на тему "Primal-dual Subgradient Method with Dual Coordinate Update".

In this talk we consider a primal-dual method for solving nonsmooth constrained optimization problem with functional constraints. This method consists in alternating updates of primal and dual variables, such that one of them can be seen as a coordinate descent scheme. Nevertheless, it has best possible performance guarantees. We show that such a method can be applied to sparse problems of very big size, ensuring the logarithmic dependence of iteration complexity in the problem’s dimension. 

В 18-30 профессор Джеонг Хан Ким прочтет лекцию на тему "A tale of models for random graphs".

Since Erdos–Renyi introduced random graphs in 1959, two closely related models for random graphs have been extensively studied. In the G(n,m) model, a graph is chosen uniformly at random from the collection of all graphs that have n vertices and m edges. In the G(n,p) model, a graph is constructed by connecting each pair of two vertices randomly. Each edge is included in the graph G(n,p) with probability p independently of all other edges.
Researchers have studied when the random graph G(n,m) (or G(n,p), resp.) satisfies certain properties in terms of n and m (or n and p, resp.). If G(n,m) (or G(n,p), resp.) satisfies a property with probability close to 1, then one may say that a `typical graph’ with m edges (or expected edge density p, resp.) on n vertices has the property. Random graphs and their variants are also widely used to prove the existence of graphs with certain properties. In this talk, a well-known problem for each of these categories will be discussed.
First, a new approach will be introduced for the problem of the emergence of a giant component of G(n,p), which was first considered by Erdos–Renyi in 1960. Second, a variant of the graph process G(n,1), G(n,2), …, G(n,m), … will be considered to find a tight lower bound for Ramsey number R(3,t) up to a constant factor.
No prior knowledge of graph theory is needed in this talk.
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