Optimization Theory

Hubertus Th. Jongen, Klaus Meer, Eberhard Triesch (Autoren)

Buch | Softcover

443 Seiten

2013 | Softcover reprint of the original 1st ed. 2004
Springer-Verlag New York Inc.
978-1-4757-8885-3 (ISBN)

Artikel merken

Optimization Theory is becoming a more and more important mathematical as well as interdisciplinary area, especially in the interplay between mathematics and many other sciences like computer science, physics, engineering, operations research, etc.
This volume gives a comprehensive introduction into the theory of (deterministic) optimization on an advanced undergraduate and graduate level. One main feature is the treatment of both continuous and discrete optimization at the same place. This allows to study the problems under different points of view, supporting a better understanding of the entire field.
Audience: The book can be adapted well as an introductory textbook into optimization theory on a basis of a two semester course; however, each of its parts can also be taught separately. Many exercises are included to increase the reader's understanding.

Optimality Criteria on Simple Regions.- Constraints, Lagrange Function, Optimality Criteria.- Parametric Aspects, Semi-Infinite Optimization.- Convex Functions, Duality, Separation Theorem.- Linear Inequalities, Constraint Qualifications.- Linear Programming: The Simplex Method.- The Ellipsoid Method.- The Method of Karmarkar for Linear Programming.- Order of Convergence, Steepest Descent, (Lagrange -)Newton.- Conjugate Direction, Variable Metric.- Penalty-, Barrier-, Multiplier-, Interior Point-Methods.- Search Methods without Derivatives.- One-Dimensional Minimization.- Graphs and Networks.- Flows in Networks.- Applications of the Max-Flow Min-Cut Theorem.- Integer Linear Programming.- Computability; the Turing machine.- Complexity theory.- Reducibility and NP-completeness.- Some NP-completeness results.- The Random Access Machine.- Complexity Theory over the Real Numbers.- Approximating NP-hard Problems.- Approximation Algorithms for TSP.- Approximation algorithms for Bin Packing.- A FPTAS for Knapsack.- Miscellaneous.

Zusatzinfo	XI, 443 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
ISBN-10	1-4757-8885-1 / 1475788851
ISBN-13	978-1-4757-8885-3 / 9781475788853
Zustand	Neuware