Optimierung für Ingenieure (mit Praktikum) (OptIngVP)7.5 ECTS
(englische Bezeichnung: Optimization for Engineers (with Laboratory))
(Prüfungsordnungsmodul: Optimierung für Ingenieure mit Praktikum)

Lehrveranstaltungen:

• • Optimization for Engineers
    (Vorlesung mit Übung, 3 SWS, Johannes Hild, Do, Fr, 10:15 - 11:45, Zoom-Meeting)
  • Programming Discussion for Optimization for Engineers
    (Übung, 1 SWS, Johannes Hild, Same room/timeslot as Optimization for Engineers)

Empfohlene Voraussetzungen:

Requires contents of the lecture Mathematics for Engineers I, II and III. Especially:

• Linear algebra

• Analysis of real valued functions

• Differential and integral calculus in multi dimensional spaces
  

Requires basic knowledge in the implementation of algorithms and data structures in a development environment.

Inhalt:

Introduction to continuous optimization problems and methods with and without constraints

• Classification of problem types

• Optimality conditions and termination criterions

• Descent directions and line search methods

• Convergence analysis
  

Unconstrained optimization

• Steepest descent and conjugate gradient

• Newton-type methods

• Nonlinear Least Squares
  

Constrained optimization

• Projection methods

• Trust Region

• Barrier and penalty methods

• Interior point methods
  

Outlook

• Noisy functions

• Modelling approaches
  

Laboratory

• Implementation of optimization algorithms

• Algorithmic optimization of test problems

• Solving a benchmark problem

Lernziele und Kompetenzen:

Wissen

• Students list requirements, strengths and weaknesses of common optimization methods.

• Students recognize crucial components in existence and convergence proofs in the context of minimizing sequences.

• Students identify optimization routines written in a programming language.
  

Verstehen

• Students explain the different components of optimization methods.

• Students describe the relationship between requirements and conclusions of existence and convergence theorems in the context of minimizing sequences.

Anwenden

• Students check feasibility, well-posedness and constraint qualifications of optimization problems.

• Students formulate and solve optimality conditions analytically.

• Students apply optimization algorithms to optimization problems.
  

Analysieren

• Students analyse uncommon optimization approaches and extract their requirements, strengths and weaknesses.

• Students observe the behavior of common optimization algorithms applied to numerical test problems.

Evaluieren (Beurteilen)

• Students evaluate the class and structure of unsolved optimization problems.

• Students choose suitable algorithmic approaches for unsolved optimization problems.

Erschaffen

• Students formulate optimization problems using mathematical methods and structures.

• Students modify and combine common optimization routines to create project-specific algorithms for unsolved optimization problems.

• Students plan and implement optimization algorithms in a programming language.

Literatur:

Nocedal, Jorge and Wright, Stephen J.: Numerical Optimization. Springer Serie in Operations Research, 2006.
Kelley, C. T.: Iterative Methods for Optimization. Frontiers in Applied Mathematics 18, SIAM Philadelphia 1999;
Polak, E.: Optimization. Algorithms and Consistent Approximations.Applied Mathematical Sciences, Volume 124, Springer-Verlag New York, 1997.
Jarre, F.:Optimierung, Springer 2003;

Bemerkung:

This module aims at students of the Faculty of Engineering of all disciplines and is suitable as an elective subject in the Bachelor's and Master's degree.

Weitere Informationen:

Verwendbarkeit des Moduls / Einpassung in den Musterstudienplan:

1. Computational Engineering (Rechnergestütztes Ingenieurwesen) (Master of Science)
   (Po-Vers. 2013 | TechFak | Computational Engineering (Rechnergestütztes Ingenieurwesen) (Master of Science) | Gesamtkonto | Wahlpflichtbereich Angewandte Mathematik | Optimierung für Ingenieure mit Praktikum)

Studien-/Prüfungsleistungen:

Optimierung für Ingenieure (Prüfungsnummer: 40501)

(englischer Titel: Optimization for Engineers)

Prüfungsleistung, Klausur, Dauer (in Minuten): 90, benotet

Anteil an der Berechnung der Modulnote: 100.0 %

Prüfungssprache: Englisch

Erstablegung: SS 2021, 1. Wdh.: WS 2021/2022

1. Prüfer:

Johannes Hild

Termin: 17.07.2021, 09:30 Uhr, Ort: H11 in Cauerstr. 11 and H9 in MHB (via Cauerstr. 11) in Erlangen
Termin: 12.02.2022, 09:30 Uhr, Ort: client_id=StudOnExamWS2021
Termin: 01.08.2022, 10:15 Uhr, Ort: client_id=StudOnExamSS2022
Termin: 01.08.2022, 10:15 Uhr, Ort: client_id=StudOnExamSS2022

Optimierung für Ingenieure - Übungen (Prüfungsnummer: 40602)

(englischer Titel: Optimization for Engineers - Laboratory)

Studienleistung, Übungsleistung, unbenotet

weitere Erläuterungen:
Aquired by completing and testing optimization algorithms. Templates are provided by the lecturer, solution files are returned using StudOn. Each student has to pass an electronic examination (multiple choice) to verify the individual competence gain.

Prüfungssprache: Englisch

Erstablegung: SS 2021

1. Prüfer:

Johannes Hild