# 376.058 Optimization This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2022W 2021W 2020W 2019W 2018W 2017W 2016W 2015W 2014W 2013W

2022W, VU, 3.0h, 4.5EC

## Properties

• Semester hours: 3.0
• Credits: 4.5
• Type: VU Lecture and Exercise
• Format: Presence

## Learning outcomes

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 mathematical 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.

## Subject of course

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:
fundamentals 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, direct vs. indirect methods, singular arcs

## Teaching methods

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.

## Mode of examination

Oral

This course consists of lectures and exercises. All events are held in presence. If necessary, a switch to distance learning is possible on short notice.

• Lecture: All lectures are held in presence at the times given in Course dates. The first lecture (including a preview on the organization of the course) starts on 4.10.2022 at 8:00.

• Exercise: All four exercises are held as presence learning events in the computer lab of the institute ACIN (room CA0426). Each exercise consists of two parts. 1) Review and discussion of prepared problems, which are the basis for the presence event and which have to be solved beforehand. 2) Solution of further problems and in parts test on lab experiments.

Each exercise is scheduled for two hours and is offered with the same contents at two different dates. It is thus sufficient to attend one event per exercise.

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).

## Course dates

DayTimeDateLocationDescription
Tue08:00 - 10:0004.10.2022 - 24.01.2023EI 1 Petritsch HS Lecture
Tue08:00 - 10:0015.11.2022EI 10 Fritz Paschke HS - UIW Lecture
Tue10:00 - 10:3029.11.2022 - 10.01.2023EI 1 Petritsch HS Lecture
Optimization - Single appointments
DayDateTimeLocationDescription
Tue04.10.202208:00 - 10:00EI 1 Petritsch HS Lecture
Tue11.10.202208:00 - 10:00EI 1 Petritsch HS Lecture
Tue18.10.202208:00 - 10:00EI 1 Petritsch HS Lecture
Tue25.10.202208:00 - 10:00EI 1 Petritsch HS Lecture
Tue08.11.202208:00 - 10:00EI 1 Petritsch HS Lecture
Tue15.11.202208:00 - 10:00EI 10 Fritz Paschke HS - UIW Lecture
Tue22.11.202208:00 - 10:00EI 1 Petritsch HS Lecture
Tue29.11.202208:00 - 10:00EI 1 Petritsch HS Lecture
Tue29.11.202210:00 - 10:30EI 1 Petritsch HS Lecture
Tue06.12.202208:00 - 10:00EI 1 Petritsch HS Lecture
Tue06.12.202210:00 - 10:30EI 1 Petritsch HS Lecture
Tue13.12.202208:00 - 10:00EI 1 Petritsch HS Lecture
Tue13.12.202210:00 - 10:30EI 1 Petritsch HS Lecture
Tue10.01.202308:00 - 10:00EI 1 Petritsch HS Lecture
Tue10.01.202310:00 - 10:30EI 1 Petritsch HS Lecture
Tue17.01.202308:00 - 10:00EI 1 Petritsch HS Lecture
Tue24.01.202308:00 - 10:00EI 1 Petritsch HS Lecture

## Examination modalities

The performance is evaluated in an oral exam in presence, 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. In case of need, the exam can be done via online video conference.

## Group dates

GroupDayTimeDateLocationDescription
Gruppe ATue10:45 - 12:4529.11.2022 Computerlabor E376, CA0426376.058 Optimization Exercise 1 Group A
Gruppe ATue10:45 - 12:4520.12.2022 Computerlabor E376, CA0426376.058 Optimization Exercise 2 Group A
Gruppe ATue10:45 - 12:4510.01.2023 Computerlabor E376, CA0426376.058 Optimization Exercise 3 Group A
Gruppe ATue10:45 - 12:4524.01.2023 Computerlabor E376, CA0426376.058 Optimization Exercise 4 Group A
Gruppe BWed13:15 - 15:1530.11.2022 Computerlabor E376, CA0426376.058 Optimization Exercise 1 Group B
Gruppe BWed13:15 - 15:1521.12.2022 Computerlabor E376, CA0426376.058 Optimization Exercise 2 Group B
Gruppe BWed13:15 - 15:1511.01.2023 Computerlabor E376, CA0426376.058 Optimization Exercise 3 Group B
Gruppe BWed13:15 - 15:1525.01.2023 Computerlabor E376, CA0426376.058 Optimization Exercise 4 Group B

## Course registration

Use Group Registration to register.

## Group Registration

GroupRegistration FromTo
Gruppe A02.10.2022 00:0115.11.2022 23:59
Gruppe B02.10.2022 00:0115.11.2022 23:59

## Curricula

Study CodeObligationSemesterPrecon.Info
066 453 Biomedical Engineering Not specified
066 503 Electrical power engineering and sustainable energy systems Mandatory elective
066 504 Master programme Embedded Systems Mandatory elective3. Semester
066 506 Energy Systems and Automation Technology Not specified3. Semester
066 507 Telecommunications Not specified3. Semester
066 515 Automation and Robotic Systems Mandatory elective
066 938 Computer Engineering Mandatory elective