应用数学青年讨论班（午餐会）——Symplectic Discretization Approach for Developing New Proximal Point Algorithm

摘要:

With the growing demand for solving high-dimensional statistical and machine learning problems, effectively solving these problems has become increasingly critical. Many effective algorithms for solving these problems have been found to be closely related to a root-finding algorithm known as the Proximal Point Algorithm (PPA). It has been established that the worst-case convergence rate of PPA is O(1/k), which may lead to slow numerical convergence. Consequently, accelerated PPAs with faster convergence rates have garnered significant interest. In this talk, we will introduce some existing accelerated PPAs and their theoretical results. Furthermore, we will present a novel approach to accelerating PPA, which we term the Symplectic PPA. This method is derived by applying the Symplectic Euler Method to discretize a first-order ODE. Theoretically, we prove that the convergence rate of Symplectic PPA is essentially o(1/k2) and that the sequence generated by Symplectic PPA converges weakly to the solution set. Our numerical experiments demonstrate that our method exhibits a faster numerical convergence rate and milder oscillation phenomena.

报告人简介:

张亦，中国科学院数学与系统科学研究院在读直博生，导师为袁亚湘研究员。目前从事的研究方向为加速一阶算法。

报名问卷：

我们提供午餐（报告时间12:30-13:00，午餐从11:45开始提供），需要预定午餐的老师同学请填报名问卷（如下），周二下午3点截止。

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