Synopses & Reviews
This book provides a systematic treatment of algebraic and topological properties of convex sets (possibly non-closed or unbounded) in the n-dimensional Euclidean space. Topics under consideration include general properties of convex sets and convex hulls, cones and conic hulls, polyhedral sets, the extreme structure, support and separation properties of convex sets.
Lectures on Convex Sets is self-contained and unified in presentation. The book grew up out of various courses on geometry and convexity, taught by the author for more than a decade. It can be used as a textbook for graduate students and even ambitious undergraduates in mathematics, optimization, and operations research. It may also be viewed as a supplementary book for a course on convex geometry or convex analysis, or as a source for independent study of the subject, suitable for non-geometers.
Contents:
The Affine Structure of ℝn
Convex Sets
Convex Hulls
Convex Cones and Conic Hulls
Recession and Normal Directions
Support and Separation Properties
The Extreme Structure of Convex Sets
The Exposed Structure of Convex Sets
Polyhedra
Readership: Graduate students in mathematics, optimization and operations research.
Review
Of the many subdisciplines of convex geometry, says Soltan, algebraicand topological properties of convex sets in the Euclidean space Rn have a place apart because they serve the whole convex geometry andare wisely used in various mathematical disciplines. He presents a systematic treatment of them in lectures on the affine structure ofRn, convex sets, convex hulls, convex cones and conic hulls, recession and normal directions, support and separation properties,the extreme structure of convex sets, the exposed structure of convex sets, and polyhedra. He appends solutions to exercises.Annotation ©2015 Ringgold, Inc., Portland, OR (protoview.com)
Review
"This is an extremely complete book on the fundamentals of the algebraic and topological properties of convex sets. This is a well-written book, which should be of considerable use to researchers in convex geometry."
Zentralblatt MATH
Review
"The book is carefully written and should be useful as a textbook for courses on convex geometry … Also of interest are the notes after each chapter. More of these would be appreciated by an expert reader. The exercises are a treasure. The book serves its purpose well and can be recommended without reservation."
Mathematical Reviews Clippings