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Cones and Duality

Charalambos D. Aliprantis Purdue University, West Lafayette, IN
Rabee Tourky The University of Queensland, Brisbane, Queensland, Australia
Available Formats:
Hardcover ISBN: 978-0-8218-4146-4
Product Code: GSM/84
List Price: $64.00 MAA Member Price:$57.60
AMS Member Price: $51.20 Electronic ISBN: 978-1-4704-2114-4 Product Code: GSM/84.E List Price:$60.00
MAA Member Price: $54.00 AMS Member Price:$48.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $96.00 MAA Member Price:$86.40
AMS Member Price: $76.80 Click above image for expanded view Cones and Duality Charalambos D. Aliprantis Purdue University, West Lafayette, IN Rabee Tourky The University of Queensland, Brisbane, Queensland, Australia Available Formats:  Hardcover ISBN: 978-0-8218-4146-4 Product Code: GSM/84  List Price:$64.00 MAA Member Price: $57.60 AMS Member Price:$51.20
 Electronic ISBN: 978-1-4704-2114-4 Product Code: GSM/84.E
 List Price: $60.00 MAA Member Price:$54.00 AMS Member Price: $48.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$96.00 MAA Member Price: $86.40 AMS Member Price:$76.80
• Book Details

Volume: 842007; 279 pp
MSC: Primary 46; 47; Secondary 06; 28; 91;

Ordered vector spaces and cones made their debut in mathematics at the beginning of the twentieth century. They were developed in parallel (but from a different perspective) with functional analysis and operator theory. Before the 1950s, ordered vector spaces appeared in the literature in a fragmented way. Their systematic study began around the world after 1950 mainly through the efforts of the Russian, Japanese, German, and Dutch schools.

Since cones are being employed to solve optimization problems, the theory of ordered vector spaces is an indispensable tool for solving a variety of applied problems appearing in several diverse areas, such as engineering, econometrics, and the social sciences. For this reason this theory plays a prominent role not only in functional analysis but also in a wide range of applications.

This is a book about a modern perspective on cones and ordered vector spaces. It includes material that has not been presented earlier in a monograph or a textbook. With many exercises of varying degrees of difficulty, the book is suitable for graduate courses.

Most of the new topics currently discussed in the book have their origins in problems from economics and finance. Therefore, the book will be valuable to any researcher and graduate student who works in mathematics, engineering, economics, finance, and any other field that uses optimization techniques.

Graduate students and research mathematicians interested in functional analysis and applications, in particular to optimization.

• Chapters
• Chapter 1. Cones
• Chapter 2. Cones in topological vector spaces
• Chapter 3. Yudin and pull-back cones
• Chapter 4. Krein operators
• Chapter 5. $\mathcal {K}$-lattices
• Chapter 6. The order extension of $L’$
• Chapter 7. Piecewise affine functions
• Chapter 8. Appendix: Linear topologies

• Reviews

• ...the book will be valuable not only for students and researchers in mathematics but also for those interested in economics, finance and engineering.

• As a whole, this book is an excellent reference of general interest in ordered vector spaces.

Mathematical Reviews
• This book will find its grateful readership as it bridges the gap between the theory of ordered vector spaces as cultivated in functional analysis and the theory of positivity as requested in applications to economics.

Zentralblatt MATH
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 842007; 279 pp
MSC: Primary 46; 47; Secondary 06; 28; 91;

Ordered vector spaces and cones made their debut in mathematics at the beginning of the twentieth century. They were developed in parallel (but from a different perspective) with functional analysis and operator theory. Before the 1950s, ordered vector spaces appeared in the literature in a fragmented way. Their systematic study began around the world after 1950 mainly through the efforts of the Russian, Japanese, German, and Dutch schools.

Since cones are being employed to solve optimization problems, the theory of ordered vector spaces is an indispensable tool for solving a variety of applied problems appearing in several diverse areas, such as engineering, econometrics, and the social sciences. For this reason this theory plays a prominent role not only in functional analysis but also in a wide range of applications.

This is a book about a modern perspective on cones and ordered vector spaces. It includes material that has not been presented earlier in a monograph or a textbook. With many exercises of varying degrees of difficulty, the book is suitable for graduate courses.

Most of the new topics currently discussed in the book have their origins in problems from economics and finance. Therefore, the book will be valuable to any researcher and graduate student who works in mathematics, engineering, economics, finance, and any other field that uses optimization techniques.

Graduate students and research mathematicians interested in functional analysis and applications, in particular to optimization.

• Chapters
• Chapter 1. Cones
• Chapter 2. Cones in topological vector spaces
• Chapter 3. Yudin and pull-back cones
• Chapter 4. Krein operators
• Chapter 5. $\mathcal {K}$-lattices
• Chapter 6. The order extension of $L’$
• Chapter 7. Piecewise affine functions
• Chapter 8. Appendix: Linear topologies
• ...the book will be valuable not only for students and researchers in mathematics but also for those interested in economics, finance and engineering.