Bài giảng về Giải tích biến phân, Quy hoạch toán học, Điều khiển tối ưu
Thời gian: 9:30-11:30, 10/12/2018

Địa điểm: Hội trường 301, nhà A5, Viện Toán học, 18 Hoàng Quốc Việt, Hà Nội

9:30-10:20: Bài giảng 1 “Criticality of Lagrange Multipliers in Variational Systems

Người giảng: Giáo sư Boris Mordukhovich (Wayne State University, Detroit, MI, USA; http://www.math.wayne.edu/~boris), Tiến sĩ Danh dự của Viện Hàn lâm Khoa học và Công nghệ Việt Nam

Tóm tắt nội dung: This talk concerns the study of criticality of Lagrange multipliers in variational systems that have been recognized in both theoretical and numearical aspects of optimization and variational analysis. In contrast to the previous developments dealing with polyhedral KKT systems and the like, we now focus on general nonpolyhedral systems that are associated, in particular, with problems of conic programming. Developing a novel approach, which is mainly based on advanced techniques and tools of second-order variational analysis and generalized differentiation, allows us to overcome principal challenges of nonpolyhedrality and to establish complete characterizations on noncritical multipliers in such settings.

Based on joint work with Ebrahim Sarabi (Miami University, Oxford, OH, USA)

10:20-10:40: Tiệc trà

10:40-11:30: Bài giảng 2 “Bioremediation of Water Resources: An Optimal Control Approach”

Người giảng: Giáo sư Hector Ramírez Cabrera (Universidad de Chile, Santiago, Chile; http://www.dim.uchile.cl/~hramirez)

Tóm tắt nội dung: This talk deals with the bioremediation, in minimal time, of a water resource (such as lakes, reservoirs, etc.) using a single continuous bioreactor. The bioreactor is connected to the reservoir through several pumps. Typically, one pump extracts polluted water and other on injects back sufficiently clean water with the same flow rate. However, we also analyze more complex pumps configurations. So, we state minimal-time optimal control problems where the control variables are related to the inflow rates of the pumps. For those problems, we analyze the existence of their solutions as well as their optimal synthesis (via Pontryagin’s principle). We also obtain, for some pumps configurations, explicit expressions of their value functions via Hamilton-Jacobi-Bellman techniques.