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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...
Central limit theorem for partial linear eigenvalue statistics of Wigner matrices
Central limit theorem partial linear eigenvalue statistics Wigner matrices Probability
2012/6/19
In this paper, we study the complex Wigner matrices $M_n=\frac{1}{\sqrt{n}}W_n$ whose eigenvalues are typically in the interval $[-2,2]$. Let $\lambda_1\leq \lambda_2...\leq\lambda_n$ be the ordered e...
Cellular Automata Rules and Linear Numbers
Cellular Automata linear and non-linear rules linear and non-linear numbers
2012/4/27
In this paper, linear Cellular Automta (CA) rules are recursively generated using a binary tree rooted at "0". Some mathematical results on linear as well as non-linear CA rules are derived. Integers ...
Some Norm Estimates for Semimartingales--- Under Linear and Nonlinear Expectations
Martingale semimartingale quasimartingale G-expectation G-martingale G-semimartingale Doob-Meyer decompostition
2011/9/15
Abstract: In this paper we introduce two types of norms for semimartingales, under both linear and nonlinear expectations. The first norm is motivated by quasimartingales, and characterizes square int...
A linear stochastic differential equation driven by a fractional Brownian motion with Hurst parameter >1/2
Linear stochastic differential equation Fractional Brownian motion Stochastic calculus Ito formula
2011/9/15
Abstract: Given a fractional Brownian motion \,\,$(B_{t}^{H})_{t\geq 0}$,\, with Hurst parameter \,$> 1/2$\,\,we study the properties of all solutions of \,\,: {equation} X_{t}=B_{t}^{H}+\int_0^t X_{u...
Existence of Linear-Quadratic Regulator for Degenerate Diffusions
Stochastic differential equation Hamilton-Jacobi-Bellman equation Linear-Quadratic problem Viscosity solutions Applications to control theory
2010/2/26
This paper studies a linear regulatory quadratic control problem for degenerate Hamilton-Jacobi-Bellman (HJB) equation. We establish the existence of a unique viscosity and a classical solution of the...