Optimierung für Ingenieure (OptIngV)5 ECTS
(englische Bezeichnung: Optimization for Engineers)
(Prüfungsordnungsmodul: Optimierung für Ingenieure)

Lehrveranstaltungen:

• • Optimierung für Ingenieure (Optimization for Engineers)
    (Vorlesung mit Übung, 3 SWS, Johannes Hild, Mo, 10:15 - 11:45, K1-119; Mi, 12:15 - 13:45, K1-119; Einzeltermin am 27.6.2018, 12:15 - 13:45, KS II; Laboratory is scheduled instead of lecture at five mondays. For schedule see StudOn.)

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

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
  

Outlook

• Linear programming and simplex method

• Integer programming

• Noisy functions

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.
  

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.

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.
  

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;
Hamacher, H.W. and K. Klamroth, K.:Linear and Network Optimization: bilingual textbook. Vieweg 2000

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. Life Science Engineering (Master of Science)
   (Po-Vers. 2015w | TechFak | Life Science Engineering (Master of Science) | 1.-2. Wahlpflichtmodul (ohne Praktikum) | Optimierung für Ingenieure)

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 2018, 1. Wdh.: WS 2018/2019

1. Prüfer:

Johannes Hild

Termin: 16.07.2018, 13:30 Uhr, Ort: Hörsaal H11
Termin: 22.02.2019, 13:30 Uhr, Ort: H12
Termin: 29.07.2019, 13:30 Uhr, Ort: Erlangen, Cauerstraße 11, Hörsaal H11
Termin: 20.02.2020, 13:30 Uhr, Ort: H12