The aim of this course is to learn the basics and the corresponding methods of static and dynamic optimization with and without constraints. The course is based on thorough mathematical concepts and focusses on the solution of specific optimization problems in the field of automatic control.

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

• Exercises:
  Four exercise courses will be offered in the computer laboratory of the institute, each with a duration of 2 hours. These exercises are not mandatory but their contents is 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 organization of this course and the dates of the exercise courses will be discussed in the first lecture.

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.