Applied Numerical Optimization

Lecturer: Prof. Alexander Mitsos, Ph.D.
Lecture: 2 hrs
Tutorials: 2 hrs
Course schedule: Please get them from the course calendar RWTHOnline
Lecture notes: Available on Moodle
Semester: Winterterm
Language: English
Exam: oral (ECTS: 4)

Computer-aided optimization methods are becoming increasingly important in all fields of engineering. In this course, the fundamental mathematical and computational concepts of optimization are introduced and explored through real-life examples – some of them are from our groups own research. The course is organized in three parts:

1. Unconstrained Optimization

We develop and intuitive understanding of the optimality conditions and study the fundamental solution methods of "Line Search" and "Trust Region". Common algorithms like steepest descent, Newton’s method and its variants, and trust-region methods are presented and tested hands-on in the Python lab.

2. Constrained Optimization

The Karush-Kuhn-Tucker (KKT) optimality conditions are derived and intensively discussed. We then look at Linear Programs as an important sub-class of constrained optimization problems. The Simplex method and the Primal-Dual interior point method are presented and visualized in the Python lab. Finally, the penalty, log-barrier and SQP methods are presented for non-linear problems.

3. Special Optimization Problems

The fundamental backgrounds of mixed-integer, global and dynamical optimization problems are introduced and discussed using examples from current research. We also look at optimization with machine learning models embedded and finally, optimization under uncertainty.

The material of the lecture course is explored in the laboratory course using Python in Jupyter Notebooks.

The course is also available on edX as “Mathematical Optimization for Engineers”. However, RWTH students can get credits only by registering for the exam on RWTHonline and upon passing.