How to Cite

Rannacher, Rolf: Lineare Optimierung: Numerik linearer und konvexer nichtlinearer Optimierungsaufgaben, Heidelberg: Heidelberg University Publishing, 2018 (Lecture Notes). https://doi.org/10.17885/heiup.417

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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Identifiers

https://doi.org/10.17885/heiup.417
ISBN 978-3-947732-04-3 (PDF)
ISBN 978-3-947732-05-0 (Softcover)

Published

11/22/2018

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Authors

Rolf Rannacher

Lineare Optimierung

Numerik linearer und konvexer nichtlinearer Optimierungsaufgaben

Lecture Notes

This introductory text is based on courses within a multi-semester cycle on “Numerical Mathematics” given by the author at the Universities in Saarbrücken and Heidelberg. In the present part basic concepts of numerical methods are presented for solving linear optimization problems (so-called “Linear Programming”). This includes besides the classical ”Simplex method“ also modern ”Interior-point methods“. As natural extensions methods for convex nonlinear, especially quadratic, optimization problems are discussed. Theoretical as well as practical aspects are considered. As prerequisite only that prior knowledge is required, which is usually taught in the introductory Analysis, Linear Algebra, and Numerics courses. For facilitating self-learning the book contains theoretical and practical exercises with solutions collected in the appendix.

Retired Professor of Numerical Mathematics at Heidelberg University – study of Mathematics at the University of Frankfurt/Main, doctorate 1974, postdoctorate 1978 at Bonn University – 1979/1980 Vis. Assoc. Professor at the University of Michigan (Ann Arbor, USA), thereafter Professor at Erlangen and Saarbrücken, in Heidelberg since 1988 – field of interest “Numerics of Partial Differential Equations”, especially the “Finite Element Method” and its applications in the Natural Sciences and Engineering; more than 160 scientific publications.

Chapters

Table of Contents
Pages
PDF
Titelei
Inhaltsverzeichnis
v–vii
Literaturverzeichnis
ix–x
0 Einleitung
1–8
1 Lineare Programme und Dualitätstheorie
9–23
2 Das Simplex-Verfahren
25–57
3 Ganzzahlige Optimierung
59–69
4 Innere-Punkte-Methoden
71–100
5 Nichtlineare Optimierungsaufgaben
101–119
6 Verfahren für nichtlineare Optimierungsaufgaben
121–158
A Lösungen der Übungsaufgaben
159–198
Index
199–201

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