走向现代数学学术报告 - 张海森教授（No. 848)

报告题目：Convergence of Newton's Method for Nonlinear Deterministic Optimal Control Problems

报告时间：2025年11月4日 11:00

腾讯会议ID：353 698 792

报 告 人：张海森 教授（四川师范大学）

邀 请 人：段月亮 博士

报告摘要：In this talk, we will discuss the convergence of Newton's algorithm for general nonlinear deterministic optimal control problems. Here, the control system is a deterministic nonlinear ordinary differential equation. We first proved the second-order differentiability of the cost functional under appropriate conditions and provided an accurate characterization of the second-order derivative of the cost functional with respect to the control in L^2 space. The local quadratic convergence rate of the Newton's algorithm is proved under a proper second-order sufficient condition for optimal controls in L^2 space. Compared to previous work, the second-order sufficient conditions in L^2 space are weaker and easier to verify.

报告人简介：张海森，四川师范大学教授，博士生导师，霍英东青年教师奖获得者。主要研究领域为随机优化与控制，在 SIAM Review, Trans. Amer. Math. Soc.，SIAM J. Control Optim.，J. Differential Equations等期刊发表学术论文近二十篇。主持国家自然科学基金2项，省重点项目1项，参与国自科基金重点项目1项。现担任SCI 学术期刊Mathematical Control and Related Fields编委。