Scientific Publishing Lectures On Convex Sets

"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 "This is an extremely complete book on the fundamentals of the algebraic and topological properties of convex sets. This is a wellwritten book, which should be of considerable use to researchers in convex geometry." Zentralblatt Math This book provides a systematic treatment of algebraic and topological properties of convex sets (possibly nonclosed or unbounded) in the ndimensional 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 selfcontained 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 nongeometers.