After successful completion of the course, students are able to identify, understand, analyze, formulate and graphically or mathematically solve basic static and dynamic optimization problems. They especially know about the theory, the mathematically principles and various methods for an exact or iterative solution of optimization problems. After successful completion of this course, students can moreover differentiate between unconstrained and constrained optimization problems and they can select and apply the specifically appropriate solution methods. This course strengthens and deepens engineering approaches, abstract and analytical thinking, independent solution of practical optimization problems, as well as mathematical skills.

Fundamentals of optimization:
existence of minima and maxima, gradient, Hessian, convexity, convergence

Unconstrained static optimization:
optimality conditions, computer-aided optimization, line search methods, choice of the step length, principle of nested intervals, Armijo condition, Wolfe condition, gradient method, Newton method, conjugate gradient method, Quasi-Newton method, Gauss-Newton-method, trust region method, Nelder-Mead method

Static optimization with constraints:
equality and inequality constraints, sensitivity considerations, active set method, gradient projection method, reduced gradient method, penalty and barrier functions, sequential quadratic programming (SQP), local SQP, globalization of SQP

Dynamic optimization:
basics of the calculus of variations, optimality conditions, Euler-Lagrange equations, Weierstrass-Erdmann conditions, design of optimal control solutions, minimum principle of Pontryagin,  energy-optimal, ressource-optimal, time-optimal, Bang-Bang control, singular arcs

The contents of this lecture are elaborated and discussed based on lecture notes and exercise notes (both documents freely available). The material is presented on the blackboard and with slides. To deepen, reinforce, and practically apply the material, example problems are discussed and mathematically solved. The software Matlab is used for computer-aided solution of optimization problems. In some cases, the developed solutions are practically implemented and tested on laboratory experiments.

Current information on the teaching mode in the winter semester 2020/2021

Most parts of this course are held as distance learning events. Links to ZOOM online-meetings of this course are available in the associated TUWEL course. A course registration is required to access the TUWEL course.

• Lecture: All lectures are exclusively held as online meetings via ZOOM at the times given in Course dates. The first lecture (including a preview on the organization of the course) starts on 6.10.2020 at 8:00.
  
  
• Exercise: Each exercise consists of two events. Their times are given in Course dates. Both events should be attended. For the exercises 1 and 2, both events are exclusively held as online meetings via ZOOM. For the exercises 3 and 4 the respective first event is exclusively held as online meeting via ZOOM and the respective second event is exclusively held as presence teaching event in the computer lab of the institute ACIN (room CA0426).
  
  All contents of the exercises are part of the final exam. The goal of the exercises is to apply the theoretical concepts and algorithms presented in the lecture to specific examples in the field of static and dynamic optimization. The focus lies on the use of numeric software (mainly Matlab).

The performance is evaluated in an oral exam, which can take place at any time Monday to Friday from 6:00 to 20:00. To arrange a time for the examination, send an e-mail with desired dates, times or time slots, your name, student ID number, and study code to steinboeck@acin.tuwien.ac.at.

Lecture Notes (in German) can be downloaded here.