Speaker : Shivakumar Kameswaran Abstract: Analysis and Formulation of a Class of Optimization Problems Constrained by Differential Equations The current decade is marked by the increased need for integration and more realistic models for characterizing complex systems, and a lot of effort is going into Modeling and Simulation of such systems. Many complex physical processes are modeled using a combination of differential and algebraic equations. Such models arise in myriad application areas such as biology, nano-scale processes/phenomena, medicine, energy (including fuel cells) and transport processes. With the growing appreciation for dynamic simulation of processes in various domains, optimization is a natural extension to consider. Dynamic optimization aims at optimizing systems that are governed by differential equations. From a mathematical viewpoint, a dynamic optimization problem is an optimal control problem, which formally refers to the minimization of a cost (objective) function subject to constraints that represent the dynamics of the system. The last decade has witnessed a tremendous amount of effort going into optimization of differential-algebraic equations. The focus was on developing numerical algorithms and optimization platforms, and solving interesting applications. But in order to cater to the scale and the complexity of present-day applications a number of open questions relating to the efficiency and the reliability of the associated numerical methods, problem formulation/reformulation, handling of ill-conditioned problems, and accommodation of reduced-order-models must be addressed. My Ph.D. research aims at addressing some of these issues using rigorous theoretical tools and/or characteristic examples, and at the same time, use the results for solving large-scale real-world applications to realize the benefits. In this talk, I will focus particularly on the following topics: The issue of Discretize then Optimize vs. Optimize then Discretize Reliability of Nonlinear Programming (NLP) based methodologies for solving optimal control problems Handling discrete decisions within the dynamic optimization framework Advantages of NLP-based methods for optimization of transport processes Regularization for singular optimal control problems with applications in bio-reactors Large-scale applications in reservoir engineering, fuel cell/gas turbine power generation plants, and transport processes The future of dynamic optimization lies in large-scale applications. With increased efforts in modeling and simulation of biological and nano-scale processes/phenomena, optimization is a natural extension to consider. With research efforts in the aforementioned directions, dynamic optimization is emerging as a much sought after tool for such applications.