Linear Optimization

The Simplex Workbook

Glenn Hurlbert (Autor)

Buch | Softcover

272 Seiten

2012
Springer-Verlag New York Inc.
978-1-4614-2455-0 (ISBN)

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The Subject A little explanation is in order for our choice of the title Linear Opti- 1 mization (and corresponding terminology) for what has traditionally been called Linear Programming.Theword programming in this context can be confusing and/or misleading to students. Linear programming problems are referred to as optimization problems but the general term linear p- gramming remains. This can cause people unfamiliar with the subject to think that it is about programming in the sense of writing computer code. It isn’t. This workbook is about the beautiful mathematics underlying the ideas of optimizing linear functions subject to linear constraints and the algorithms to solve such problems. In particular, much of what we d- cuss is the mathematics of Simplex Algorithm for solving such problems, developed by George Dantzig in the late 1940s. The word program in linear programming is a historical artifact. When Dantzig ?rstdevelopedthe Simplex Algorithm to solvewhat arenowcalled linear programming problems, his initial model was a class of resource - location problems to be solved for the U.S. Air Force. The decisions about theallocationswerecalled‘Programs’bytheAirForce,andhencetheterm.

The Simplex Algorithm.- Geometry.- The Duality Theorem.- Matrix Environment.- General Form.- Unsolvable Systems.- Geometry Revisited.- Game Theory.- Network Environment.- Combinatorics.- Economics.- Integer Optimization.

Reihe/Serie	Undergraduate Texts in Mathematics
Zusatzinfo	40 Illustrations, black and white; XVII, 272 p. 40 illus.
Verlagsort	New York, NY
Sprache	englisch
Maße	178 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
	Mathematik / Informatik ► Mathematik ► Graphentheorie
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
	Wirtschaft ► Betriebswirtschaft / Management
Schlagworte	convex geometry • Convexity • Duality • Integer Optimization • Lineare Optimierung • linear optimization • Linear Programming • matrix games • modified Moore method • Networks • Simplex Algorithm
ISBN-10	1-4614-2455-0 / 1461424550
ISBN-13	978-1-4614-2455-0 / 9781461424550
Zustand	Neuware