Grundlehren der mathematischen Wissenschaften

Convexity and Optimization in Finite Dimensions I

Authors: Stoer, Josef, Witzgall, Christoph

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About this book

Dantzig's development of linear programming into one of the most applicable optimization techniques has spread interest in the algebra of linear inequalities, the geometry of polyhedra, the topology of convex sets, and the analysis of convex functions. It is the goal of this volume to provide a synopsis of these topics, and thereby the theoretical back­ ground for the arithmetic of convex optimization to be treated in a sub­ sequent volume. The exposition of each chapter is essentially independent, and attempts to reflect a specific style of mathematical reasoning. The emphasis lies on linear and convex duality theory, as initiated by Gale, Kuhn and Tucker, Fenchel, and v. Neumann, because it represents the theoretical development whose impact on modern optimi­ zation techniques has been the most pronounced. Chapters 5 and 6 are devoted to two characteristic aspects of duality theory: conjugate functions or polarity on the one hand, and saddle points on the other. The Farkas lemma on linear inequalities and its generalizations, Motzkin's description of polyhedra, Minkowski's supporting plane theorem are indispensable elementary tools which are contained in chapters 1, 2 and 3, respectively. The treatment of extremal properties of polyhedra as well as of general convex sets is based on the far reaching work of Klee. Chapter 2 terminates with a description of Gale diagrams, a recently developed successful technique for exploring polyhedral structures.

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $79.99
price for USA in USD (gross)
  • ISBN 978-3-642-46216-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.99
price for USA in USD
  • ISBN 978-3-642-46218-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Convexity and Optimization in Finite Dimensions I
Authors
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
163
Copyright
1970
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin · Heidelberg
eBook ISBN
978-3-642-46216-0
DOI
10.1007/978-3-642-46216-0
Softcover ISBN
978-3-642-46218-4
Series ISSN
0072-7830
Edition Number
1
Number of Pages
X, 298
Additional Information
Volume 2 has not been published
Topics