Extended mean field control
problems with constraints:
The generalized Fritz-John conditions
and Lagrangian method
报告专家：薄立军 教授（西安电子科技大学）
报告时间：5月14日（星期三）下午2:00--3:00
报告地点：线上，腾讯会议：922-203-131 会议密码：250514
报告摘要：This talk is concerned with the extended mean field control problems under general dynamic expectation constraints and/or dynamic pathwise state-control and law constraints. We aim to pioneer the establishment of the stochastic maximum principle (SMP) and the derivation of the backward SDE (BSDE) from the perspective of the constrained optimization using the method of Lagrangian multipliers. To this end, we first propose to embed the constrained extended mean-field control (C-MFC) problems into some abstract optimization problems with constraints on Banach spaces, for which we develop the generalized Fritz-John (FJ) optimality conditions. We then prove the stochastic maximum principle (SMP) for C-MFC problems by transforming the FJ type conditions into an equivalent stochastic first-order condition associated with a general type of constrained forward-backward SDEs (FBSDEs). Contrary to the existing literature, we treat the controlled Mckean-Vlasov SDE as an infinite-dimensional equality constraint such that the BSDE induced by the FJ first-order optimality condition can be interpreted as the generalized Lagrange multiplier to cope with the SDE constraint. Finally, we also present the SMP for stochastic control problems and MFG problems under similar types of constraints as consequences of our main result for C-MFC problems.
专家简介：薄立军，西安电子科技大学数学与统计学院教授，概率与数理统计专业博导、本科毕业于西安电子科技大学数学系、分别于2006年和2009年获南开大学概率论与数理统计专业理学硕士和理学博士学位。主持国家自然科学基金面上项目3项、陕西数理基础科学研究重点项目、中科院前沿科学重点研究计划项目；获2023年度陕西高等学校科学技术研究优秀成果奖特等奖(第一完成人); 在概率统计、随机控制和金融数学等领域权威学术期刊《Ann. Appl. Prob.》《Math. Oper. Res.》《Production Oper. Manag.》(UTD 24)《Math. Finan.》《Science China: Math.》《SIAM J. Contr. Optim.》《SIAM J. Finan. Math.》等发表论文70余篇。出版教材《随机过程》《哈佛概率公开课》（译著）《最优化模型》（译著）和《高等概率论》（科学出版社“十四五”高等学校本科规划教材）。
邀请人：胡泽春
