Format:
Online-Ressource (digital)
ISBN:
9780387791487
,
1280390972
,
9781280390975
Series Statement:
Undergraduate Texts in Mathematics
Content:
The Simplex Algorithm -- Geometry -- The Duality Theorem -- Matrix Environment -- General Form -- Unsolvable Systems -- Geometry Revisited -- Game Theory -- Network Environment -- Combinatorics -- Economics -- Integer Optimization.
Content:
This undergraduate textbook is written for a junior/senior level course on linear optimization. Unlike other texts, the treatment allows the use of the "modified Moore method" approach by working examples and proof opportunities into the text in order to encourage students to develop some of the content through their own experiments and arguments while reading the text. Additionally, the focus is on the mathematics underlying the ideas of optimizing linear functions under linear constraints and the algorithms used to solve them. In particular, the author uses the Simplex Algorithm to motivate these concepts. The text progresses at a gentle and inviting pace. The presentation is driven by numerous examples and illustrations. Ample exercises are provided at the end of each chapter for mastering the material. Opportunities for integrating Maple (or similar) software are included in the book. The author’s own WebSim software can be freely downloaded from his website for pedagogical use. The teacher's version of the text contains solutions embedded within the text, rather than in an appendix. It also has extra material and suggestions for the teacher’s benefit. Junior/senior level undergraduate students will benefit from the book, as will beginning graduate students. Future secondary school mathematics teachers will also find this book useful. Arizona State University Professor Glenn H. Hurlbert has published nearly 50 articles in graph theory, combinatorics, and optimization, and has been the recipient of numerous teaching and mentoring awards from ASU, the ASU Parents Association, the School of Mathematical and Statistical Sciences, and the Mathematical Association of America.
Note:
Includes bibliographical references and index
,
""Dedication""; ""Preface""; ""Contents""; ""1 Introduction""; ""1.1 The Diet Problem""; ""1.2 The Matching Problem""; ""1.3 Un Problema de la Practica""; ""1.4 Standard Form and the Dual""; ""1.5 Exercises""; ""2 The Simplex Algorithm""; ""2.1 Geometric Lens""; ""2.2 Algebraic Lens""; ""2.3 Chinese for a Little Practice""; ""2.4 Infeasible Basis""; ""2.5 Shortcut Method""; ""2.6 Infeasibility""; ""2.7 Unboundedness""; ""2.8 Cycling""; ""2.9 The Fundamental Theorem""; ""2.10 Exercises""; ""3 Geometry""; ""3.1 Extreme Points""; ""3.2 Convexity""; ""3.3 [Chinese characters]""
,
""3.4 Caratheodory�s Theorem""""3.5 Exercises""; ""4 The Duality Theorem""; ""4.1 Primal-Dual Relationship""; ""4.2 Complementary Slackness Conditions""; ""4.3 Jizoezi, Jizoezi, Jizoezi""; ""4.4 Finding Optimal Certificates""; ""4.5 Exercises""; ""5 Matrix Environment""; ""5.1 Format and Dictionaries""; ""5.2 Simplex Phases and Advantages""; ""5.3 Hebrew for Some Practice""; ""5.4 Basic Coefficients""; ""5.5 Exercises""; ""6 General Form""; ""6.1 Nonstandard Duals""; ""6.2 General Simplex and Phase 0""; ""6.3 Plus de Pratique""; ""6.4 General Duality and Slackness""; ""6.5 Exercises""
,
""7 Unsolvable Systems""""7.1 Infeasible Certificates""; ""7.2 Inconsistency""; ""7.3 Hindi for Practice this""; ""7.4 Unsolvable Subsystems""; ""8 Geometry Revisited""; ""8.1 Helly�s Theorem""; ""8.2 Permutation Matrices""; ""8.3 Pratique de Novo""; ""8.4 Cones""; ""8.5 Exercises""; ""9 Game Theory""; ""9.1 Matrix Games""; ""9.2 Minimax Theorem""; ""9.3 Bitte Praxis""; ""9.4 Saddles""; ""9.5 Exercises""; ""10 Network Environment""; ""10.1 Shipping""; ""10.2 Trees""; ""10.3 Nilai!""; ""10.4 Integrality""; ""10.5 Exercises""; ""11 Combinatorics""; ""11.1 Matchings""; ""11.2 Covers""
,
""11.3 [Chinese characters]""""11.4 Systems of Distinct Representatives""; ""12 Economics""; ""12.1 Shadow Prices""; ""12.2 Reduced Costs""; ""12.3 Gyakoroljon egy Kicsit""; ""12.4 Dual Simplex""; ""12.5 Exercises""; ""13 Integer Optimization""; ""13.1 Cutting Planes""; ""13.2 Branch-and-Bound""; ""13.3 Russian for Final Practice""; ""13.4 Integer Certificates""; ""13.5 Exercises""; ""A Linear Algebra Review""; ""B Equivalence of Auxiliary and Shortcut Methods""; ""C Complexity""; ""C.1 P versus NP""; ""C.2 Examples""; ""C.3 LO Complexity""; ""D Software""; ""D.1 WebSim""; ""D.2 Algorithms""
,
""D.3 MAPLE""""Index""
Additional Edition:
ISBN 9780387791470
Additional Edition:
Buchausg. u.d.T. Hurlbert, Glenn Linear optimization New York : Springer, 2010 ISBN 9780387791470
Additional Edition:
ISBN 9781461424550
Language:
English
Subjects:
Mathematics
Keywords:
Lineare Optimierung
;
Lineare Optimierung
DOI:
10.1007/978-0-387-79148-7
URL:
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URL:
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