Applied Numerical Optimization
|Lecturer:||Prof. Alexander Mitsos, Ph.D.|
|Course schedule:||Please get them from the course calendar RWTHOnline|
|Lecture notes:||Available on Moodle|
|Exam:||oral (ECTS: 4)|
Computer-aided optimization methods gain increasing importance in all ranges of engineering and should become the standard tool for process engineers in the near future. In this course, the fundamental mathematical concepts of optimization are introduced and explored through the use of applied examples. The course is organized in three parts:
1. Unconstrained Optimization
For unconstrained problems, the optimality conditions are derived and the fundamental solution methods of "Line Search" and "Trust Region" presented. In the “Line Search” strategy, the methods of steepest descent and conjugate gradients are highlighted, whereas for the “Trust Region” solution strategy, Newton and quasi-Newton methods are examined.
2. Constrained Optimization
For constrained optimization, the Karush-Kuhn-Tucker (KKT) optimality conditions are derived and intensively discussed. Subsequently, the solution methods are presented for special classes of problems: the simplex method of linear programming (LP) for linear problems, the quadratic programming (QP) for quadratic problems and the sequential quadratic programming (SQP) for nonlinear 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.
The material of the lecture course is explored in the laboratory course using the Matlab optimization toolbox.