报告地点：行健楼学术活动室526

邀请人：蔡邢菊教授

报告摘要：In this paper, we consider a class of state constrained linear parabolic optimal control problems. Instead of treating the inequality state constraints directly, we reformulate the problem as an equality-constrained optimization problem, and then apply the augmented Lagrangian method (ALM) to solve it. We prove the convergence of the ALM without any existence or regularity assumptions on the corresponding Lagrange multipliers, which is an essential complement to the classical theoretical results for the ALM because restrictive regularity assumptions are usually required to guarantee the existence of the Lagrange multipliers associated with the state constraints. In addition, under an appropriate choice of penalty parameter sequence, we can obtain a super-linear non-ergodic convergence rate for the ALM. Computationally, we apply a semi-smooth Newton (SSN) method to solve the ALM subproblems and design an efficient preconditioned conjugate gradient method for solving the Newton systems. Some numerical results are given to illustrate the effectiveness and efficiency of our algorithm.

个人简介：

上海大学教务部教学改革处处长、上海大学理学院教授、博士生导师。主要从事最优化与最优控制理论与算法及其在信息工程中的应用研究，在Automatica、IEEE Trans Automatic Control、J Optim Theory Appl、J Global Optim等控制、优化领域核心期刊发表论文60篇，在Springer出版学术专著一部。主持多项国家自然科学基金和上海市科委基础重点项目，并参与多项国家自然科学基金重大和重点项目。先后入选上海市青年东方学者计划，并获上海大学蔡冠深优秀青年教师奖和中国运筹学会青年科技奖提名奖。现为国际优化杂志J Indus Manag Optim编委，并任中国运筹学会理事，数学规划分会理事，中国工业与应用数学学会竞赛工作委员会委员，上海市运筹学会常务副理事长兼秘书长。