On Models, Algorithms, and Duality
Buch, Englisch, 108 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 201 g
ISBN: 978-0-387-21155-8
Verlag: Springer
Optimization is the task of finding the best member of a finite or infinite set of possible choices, based on some objective measure of the merit of each choice in the set. The three key facets of the subject are the art of constructing optimization models, the science of discovering and implementing efficient algorithms for solving optimization models, and the mathematics of optimization models and algorithms. This book provides a very gentle introduction to modeling, algorithms and duality and should appeal to several audiences at once: students (as a supplement to a regular textbook), general readers such as people in business (as an introduction to how optimization affects their everyday lives), and instructors (as a source of ideas for how to teach optimization differently).
Zielgruppe
Lower undergraduate
Autoren/Hrsg.
Weitere Infos & Material
1. Simple Motivating Examples.- 1.1 Shopping for Food.- 1.2 Watering the Garden.- 1.3 Chopping Wood.- 1.4 Going Fishing.- 1.5 Summary.- 2. A Quintessential Optimization Problem.- 2.1 Models.- 2.2 Algorithms.- 2.3 Duality.- 2.4 Notes.- 3. Duality on Bipartite Networks.- 3.1 Matching.- 3.2 Covering.- 3.3 König-Egerváry Duality.- 3.4 Notes.- 4. A Network Flow Overview.- 4.1 Problem Reformulations.- 4.2 A Network Flow Tree.- 4.3 Summary: Combinatorial vis-à-vis Continuous.- 4.4 Notes.- 5. Duality in Linear Programming.- 5.1 In the Marketplace.- 5.2 Farkas Duality and LP Optimality.- 5.3 Notes.- 6. The Golden Age of Optimization.- 6.1 Dantzig’s Simplex Algorithm.- 6.2 Linear Programming in Practice.- 6.3 Network Simplex Algorithm.- 6.4 Notes.- 7. An Algorithmic Revolution.- 7.1 Affine Scaling.- 7.2 Central Path.- 7.3 Interior-Point Algorithms.- 7.4 Notes.- 8. Nonlinear Programming.- 8.1 Geometric Perspective.- 8.2 Algebraic Perspective.- 8.3 Information Costs.- 8.4 Dimensions.- 8.5 Constraints.- 8.6 Differentiable Programming.- 8.7 Notes.- 9. DLP and Extensions.- 9.1 A Timber-Harvesting Problem.- 9.2 A Rangeland Improvement Problem.- 9.3 Resource-Decision Software.- 9.4 Notes.- 10. Optimization: The Big Picture.- 10.1 A “Cubist” Portrait.- 10.2 Notes.- References.- About the Author.
