Algorithmic Principles of Mathematical Programming

1. Auflage. Softcover version of original hardcover Auflage 2002
ISBN: 978-90-481-6117-1
Verlag: Springer Netherlands

Buch, Englisch, Band 24, 339 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 534 g

Reihe: Texts in the Mathematical Sciences

Algorithmic Principles of Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear programming, and nonlinear optimization are closely linked. This book offers a comprehensive introduction to the whole subject and leads the reader to the frontiers of current research. The prerequisites to use the book are very elementary. All the tools from numerical linear algebra and calculus are fully reviewed and developed. Rather than attempting to be encyclopedic, the book illustrates the important basic techniques with typical problems. The focus is on efficient algorithms with respect to practical usefulness. Algorithmic complexity theory is presented with the goal of helping the reader understand the concepts without having to become a theoretical specialist. Further theory is outlined and supplemented with pointers to the relevant literature.

Zielgruppe

Research

Autoren/Hrsg.

Faigle, Ulrich

Still, G.

Kern, W.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Operations Research Spieltheorie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik EDV | Informatik Informatik Logik, formale Sprachen, Automaten

Inhaltsverzeichnis

1. Real Vector Spaces.- 2. Linear Equations and Linear Inequalities.- 3. Polyhedra.- 4. Linear Programs and the Simplex Method.- 5. Lagrangian Duality.- 6. An Interior Point Algorithm for Linear Programs.- 7. Network Flows.- 8. Complexity.- 9. Integer Programming.- 10. Convex Sets and Convex Functions.- 11. Unconstrained Optimization.- 12. Constrained Nonlinear Optimization.- List of frequently used Symbols.