The goal of this course is to provide a basic understanding of the methods and algorithms for the static and dynamic optimization with and without constraints based on thorough mathematical concepts in order to solve 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, trust region method, Nelder-Mead method

Static optimization with constraints:
equality and inequality constraints, sensitivity considerations, active set method, gradient projection 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

• Guidelines for the exercise course:
  Four exercises will be offered in the computer laboratory of the institute, each with a duration of 2 hours. These exercises are not mandatory but the implementation of optimisation algorithms 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 using numeric programs (mainly Matlab) containing all the necessary functionality. The dates of the exercises will be fixed in the first lecture at October 3rd, 2016. Additionally, a preliminary discussion will take place 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) are available on the homepage of the institute.