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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Primal Dual Alternating Proximal Gradient Algorithms for Nonsmooth Nonconvex Minimax Problems with Coupled Linear Constraints
耦合 线性约束 非光滑 非凸极小问题 基本对偶交替 近端梯度算法
2023/4/14
Nonconvex minimax problems have attracted wide attention in machine learning, signal processing and many other fields in recent years. In this paper, we propose a primal dual alternating proximal grad...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Deep image prior for inverse problems: acceleration and probabilistic treatment
反问题 深度图像 加速 概率处理
2023/5/10
Since its first proposal in 2018, deep image prior has emerged as a very powerful unsupervised deep learning technique for solving inverse problems. The approach has demonstrated very encouraging empi...
UNIVERSAL POISSON AND NORMAL LIMIT THEOREMS IN GRAPH COLORING PROBLEMS WITH CONNECTIONS TO EXTREMAL COMBINATORICS
Limit theorem the monochromatic edge evenly random colors random graph
2015/7/7
This paper proves limit theorems for the number of monochromatic edges in uniform random colorings of general random graphs. The limit theorems are universal depending solely on the limiting behavior ...
G- expectation, G- normal distribution and related problems
G-expectation G-normal distribution sublinear expectation space viscosity solution classical probability theory space
2011/11/5
In this paper we study the academician Peng Shige's papers of the nonlinear expectation since 2005. Under this foundation we interpret some theories and resolve several problems of the theory of G-exp...
Schroder's problems and scaling limits of random trees
Schroder's problems Probability scaling limits of random trees
2011/8/31
Abstract: In a classic paper Schr\"oder posed four combinatorial problems about the number of certain types of bracketings of words and sets. Here we address what these bracketings look like on averag...
Optimal stopping problems for the maximum process with upper and lower caps
Optimal stopping optimal stopping boundary principle of smooth fit principle of continuous fit Levy processes
2011/8/23
Abstract: This paper concerns optimal stopping problems driven by a spectrally negative L\'evy process $X$. More precisely, we are interested in modifications of the Shepp-Shiryaev optimal stopping pr...
On Arnold's and Kazhdan's equidistribution problems
Arnold's Kazhdan's equidistribution problems
2010/12/13
We consider isometric actions of lattices in semisimple algebraic groups on (possibly non-compact) homogeneous spaces with (possibly infinite) invariant Radon measure. We assume that
the action has a...
Martingale problems on Banach spaces -- Existence, uniqueness and the Markov property
Martingale solution strong Markov property stochastic partial differential equation
2010/12/6
We study (local) martingale problems on a general separable Banach space E and apply our results to stochastic evolution equations. In particular,we prove that if such an equation is well-posed, then ...
Trace Inequalities with Applications to Orthogonal Regression and Matrix Nearness Problems
Trace inequalities stochastic matrices orthogonal regression matrix nearness problems
2010/4/16
Matrix trace inequalities are finding increased use in many areas such as analysis, where they can be used to generalise several well known classical inequalities, and computational statistics, where ...
The Optimal Order Error Estimates for Finite Element Approximations to Hyperbolic Problems
2007/12/12
In this paper, the linear finite element approximation to the positive and symmetric, linear hyperbolic systems is analyzed and an $O(h^2)$ order error estimate is established under the conditions of ...