德国亚琛工业大学Michael Herty教授
开设全英文课程的通知
为了提高研究生教学的国际化水平，系统工程研究所邀请到德国亚琛工业大学Michael Herty教授为博士研究生开设全英文课程《复杂系统建模》（课程编号：B014114），欢迎相关专业博士和硕士研究生旁听。
1、授课时间
分两个阶段：第一阶段，2011年9月19日到23日，共计5天，每天上午9:00-12:00；第二阶段，2012年2月初，具体时间待定，1～2周。
2、授课地点
太阳集团tyc539九龙湖校区纪忠楼203。
3、授课内容
Both lectures are intended for Masters and PhD students. Analysis and linear Algebra theory is required as well as some knowledge on functional analysis and partial differential equations. The lectures start with a short review of known results and continue to research questions.
Optimization C
General topic: Optimization problems with constraints given by ordinary (ODE) and partial differential equations (PDE).
Contents.
- Introduction
- Review of classical constrained optimization results in finite dimensions
- Differentiability properties of abstrakt operators given by PDEs or ODEs
- Optimal control problem for ODEs
- Pontryagins Maximum principle
- Application: Linear Time--Varying Systems and Linear Quadratic Regulators
- Dynamic Programming and Hamilton Jacobi Bellmann Equation
- Examples of PDE constrained optimization problems
- Existence of Minimizers in infinite space dimensions
- Necessary and sufficient optimality conditions in infinite space dimensions in equality constraint case
- Necessary and sufficient optimality conditions in infinite space dimensions in inequality constraint case
- Example: Variational problems or unconstrained energy minimization
- Example: Control of the heat equation
Numerical Optimization
General topic: Numerical methods for inequality and equality constrained finite dimensional optimization problems
Contents:
- Review of necessary and sufficient finite dimensional conditions
- Discussion of convex optimization problems
- General convergence results in the unconstrained case
-Methods for unconstrained optimization: Linesearch, Quasi-Newton, Newton, BFGS, DFP
-Methods for equality constrained quadratic problems: Primal projection method
- Trust-region methods: Cuachy point, adaptive cubic regularization
- SQP methods: local and global convergence, reduced SQP Newton method, Maratos effect
- Interior point methods: Barrier functions, penalty functions, perturbed KKT System, Path analysis
- Methods for linear problems: Simplex
4、Michael Herty教授简历
Michael Herty holds a professor position for Continuous Optimization since 2008 at RWTH Aachen University, Germany. Furthermore, he is the principal investigator of Aachen Institute of Advanced Study in Computational Engineering (AICES), and associated member of Center of Computational Engineering (CCES) in RWTH Aachen University. His research interest focuses on Mathematical modeling and computation using partial differential equations and its applications in supply chain, traffic flow, and gas dynamics. And he has been awarded several funds on these topics by DFG and DAAD.
