Lineare Optimierung
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Rannacher, Rolf: Lineare Optimierung: Numerik linearer und konvexer nichtlinearer Optimierungsaufgaben, Heidelberg: Heidelberg University Publishing, 2018.

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ISBN 978-3-947732-04-3 (PDF)
ISBN 978-3-947732-05-0 (Softcover)

Published 22.11.2018.


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.

0 Einleitung
1 Lineare Programme und Dualitätstheorie
2 Das Simplex-Verfahren
3 Ganzzahlige Optimierung
4 Innere-Punkte-Methoden
5 Nichtlineare Optimierungsaufgaben
6 Verfahren für nichtlineare Optimierungsaufgaben
A Lösungen der Übungsaufgaben