Scientific Publishing Lectures on Convex Sets

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 ReviewsThis 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 MATHThe book is very well written. In spite of its relatively elementary level, the book contains many important results in finite dimensional convexity, necessary in many other mathematical areas. By the detailed and rigorous presentation of the material it can be recommended for self-study as well. --Studia Universitatis Babe -Bolyai Mathematica Product Description 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. From the Back Cover 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.