Combinatorial Convexity PDF Download
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Author | : Günter Ewald |
Publisher | : Springer Science & Business Media |
Total Pages | : 378 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461240441 |
Download Combinatorial Convexity and Algebraic Geometry Book in PDF, ePub and Kindle
The book is an introduction to the theory of convex polytopes and polyhedral sets, to algebraic geometry, and to the connections between these fields, known as the theory of toric varieties. The first part of the book covers the theory of polytopes and provides large parts of the mathematical background of linear optimization and of the geometrical aspects in computer science. The second part introduces toric varieties in an elementary way.
Author | : Imre Bárány |
Publisher | : American Mathematical Soc. |
Total Pages | : 148 |
Release | : 2021-11-04 |
Genre | : Education |
ISBN | : 1470467097 |
Download Combinatorial Convexity Book in PDF, ePub and Kindle
This book is about the combinatorial properties of convex sets, families of convex sets in finite dimensional Euclidean spaces, and finite points sets related to convexity. This area is classic, with theorems of Helly, Carathéodory, and Radon that go back more than a hundred years. At the same time, it is a modern and active field of research with recent results like Tverberg's theorem, the colourful versions of Helly and Carathéodory, and the (p,q) (p,q) theorem of Alon and Kleitman. As the title indicates, the topic is convexity and geometry, and is close to discrete mathematics. The questions considered are frequently of a combinatorial nature, and the proofs use ideas from geometry and are often combined with graph and hypergraph theory. The book is intended for students (graduate and undergraduate alike), but postdocs and research mathematicians will also find it useful. It can be used as a textbook with short chapters, each suitable for a one- or two-hour lecture. Not much background is needed: basic linear algebra and elements of (hyper)graph theory as well as some mathematical maturity should suffice.
Author | : Bozzano G Luisa |
Publisher | : Elsevier |
Total Pages | : 803 |
Release | : 2014-06-28 |
Genre | : Mathematics |
ISBN | : 0080934390 |
Download Handbook of Convex Geometry Book in PDF, ePub and Kindle
Handbook of Convex Geometry, Volume A offers a survey of convex geometry and its many ramifications and relations with other areas of mathematics, including convexity, geometric inequalities, and convex sets. The selection first offers information on the history of convexity, characterizations of convex sets, and mixed volumes. Topics include elementary convexity, equality in the Aleksandrov-Fenchel inequality, mixed surface area measures, characteristic properties of convex sets in analysis and differential geometry, and extensions of the notion of a convex set. The text then reviews the standard isoperimetric theorem and stability of geometric inequalities. The manuscript takes a look at selected affine isoperimetric inequalities, extremum problems for convex discs and polyhedra, and rigidity. Discussions focus on include infinitesimal and static rigidity related to surfaces, isoperimetric problem for convex polyhedral, bounds for the volume of a convex polyhedron, curvature image inequality, Busemann intersection inequality and its relatives, and Petty projection inequality. The book then tackles geometric algorithms, convexity and discrete optimization, mathematical programming and convex geometry, and the combinatorial aspects of convex polytopes. The selection is a valuable source of data for mathematicians and researchers interested in convex geometry.
Author | : David C. Kay |
Publisher | : |
Total Pages | : 264 |
Release | : 1982 |
Genre | : Mathematics |
ISBN | : |
Download Convexity and Related Combinatorial Geometry Book in PDF, ePub and Kindle
Author | : Stephen P. Boyd |
Publisher | : Cambridge University Press |
Total Pages | : 744 |
Release | : 2004-03-08 |
Genre | : Business & Economics |
ISBN | : 9780521833783 |
Download Convex Optimization Book in PDF, ePub and Kindle
Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
Author | : Branko Grünbaum |
Publisher | : Springer Science & Business Media |
Total Pages | : 561 |
Release | : 2013-12-01 |
Genre | : Mathematics |
ISBN | : 1461300193 |
Download Convex Polytopes Book in PDF, ePub and Kindle
"The original edition [...] inspired a whole generation of grateful workers in polytope theory. Without it, it is doubtful whether many of the subsequent advances in the subject would have been made. The many seeds it sowed have since grown into healthy trees, with vigorous branches and luxuriant foliage. It is good to see it in print once again." --Peter McMullen, University College London
Author | : Daniel Hug |
Publisher | : Springer Nature |
Total Pages | : 287 |
Release | : 2020-08-27 |
Genre | : Mathematics |
ISBN | : 3030501809 |
Download Lectures on Convex Geometry Book in PDF, ePub and Kindle
This book provides a self-contained introduction to convex geometry in Euclidean space. After covering the basic concepts and results, it develops Brunn–Minkowski theory, with an exposition of mixed volumes, the Brunn–Minkowski inequality, and some of its consequences, including the isoperimetric inequality. Further central topics are then treated, such as surface area measures, projection functions, zonoids, and geometric valuations. Finally, an introduction to integral-geometric formulas in Euclidean space is provided. The numerous exercises and the supplementary material at the end of each section form an essential part of the book. Convexity is an elementary and natural concept. It plays a key role in many mathematical fields, including functional analysis, optimization, probability theory, and stochastic geometry. Paving the way to the more advanced and specialized literature, the material will be accessible to students in the third year and can be covered in one semester.
Author | : Paul J. Kelly |
Publisher | : |
Total Pages | : 0 |
Release | : 2009 |
Genre | : Convex bodies |
ISBN | : 9780486469805 |
Download Geometry and Convexity Book in PDF, ePub and Kindle
This text assumes no prerequisites, offering an easy-to-read treatment with simple notation and clear, complete proofs. From motivation to definition, its explanations feature concrete examples and theorems. 1979 edition.
Author | : Rolf Schneider |
Publisher | : Cambridge University Press |
Total Pages | : 759 |
Release | : 2014 |
Genre | : Mathematics |
ISBN | : 1107601010 |
Download Convex Bodies: The Brunn–Minkowski Theory Book in PDF, ePub and Kindle
A complete presentation of a central part of convex geometry, from basics for beginners, to the exposition of current research.
Author | : M.L.J. van de Vel |
Publisher | : Elsevier |
Total Pages | : 556 |
Release | : 1993-08-02 |
Genre | : Mathematics |
ISBN | : 0080933106 |
Download Theory of Convex Structures Book in PDF, ePub and Kindle
Presented in this monograph is the current state-of-the-art in the theory of convex structures. The notion of convexity covered here is considerably broader than the classic one; specifically, it is not restricted to the context of vector spaces. Classical concepts of order-convex sets (Birkhoff) and of geodesically convex sets (Menger) are directly inspired by intuition; they go back to the first half of this century. An axiomatic approach started to develop in the early Fifties. The author became attracted to it in the mid-Seventies, resulting in the present volume, in which graphs appear side-by-side with Banach spaces, classical geometry with matroids, and ordered sets with metric spaces. A wide variety of results has been included (ranging for instance from the area of partition calculus to that of continuous selection). The tools involved are borrowed from areas ranging from discrete mathematics to infinite-dimensional topology. Although addressed primarily to the researcher, parts of this monograph can be used as a basis for a well-balanced, one-semester graduate course.