Convexity From The Geometric Point Of View Exercises And Solutions
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Convexity From The Geometric Point Of View Exercises And Solutions
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Author : Vitor Balestro
language : en
Publisher: Springer Nature
Release Date : 2025-08-04
Convexity From The Geometric Point Of View Exercises And Solutions written by Vitor Balestro and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-04 with Mathematics categories.
This book provides the solutions to all 347 exercises contained in the text Convexity from the Geometric Point of View, published in the same Cornerstones series. All these exercises are restated and numbered analogously to those in the original text. The corresponding solutions follow each exercise. Besides the discussion of all solutions, some additional facts about the main text are sprinkled throughout. Sections of further reading are posted to the ends of each chapter supplying the reader with background literature to selected notions and tools that play a role in the exercises and/or solutions to the chapter. The original text gives a comprehensive introduction to the “common core” of convex geometry and is suitable as a primary text for courses in convex geometry and in discrete geometry (including polytopes). Additionally, it can be used as a single reference for a complete introduction to convex geometry. The content coverage is sufficiently broad that the reader may gain a glimpse of the entire breadth of the field, various subfields, and interesting connections to neighboring disciplines. Mainly directed to graduate and advanced undergraduates, the original text is self-contained in such a way that it can be read by anyone who has standard undergraduate knowledge of analysis and of linear algebra. The same is true for this book of solutions.
Convexity From The Geometric Point Of View
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Author : Vitor Balestro
language : en
Publisher: Springer Nature
Release Date : 2024-07-14
Convexity From The Geometric Point Of View written by Vitor Balestro and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-14 with Mathematics categories.
This text gives a comprehensive introduction to the “common core” of convex geometry. Basic concepts and tools which are present in all branches of that field are presented with a highly didactic approach. Mainly directed to graduate and advanced undergraduates, the book is self-contained in such a way that it can be read by anyone who has standard undergraduate knowledge of analysis and of linear algebra. Additionally, it can be used as a single reference for a complete introduction to convex geometry, and the content coverage is sufficiently broad that the reader may gain a glimpse of the entire breadth of the field and various subfields. The book is suitable as a primary text for courses in convex geometry and also in discrete geometry (including polytopes). It is also appropriate for survey type courses in Banach space theory, convex analysis, differential geometry, and applications of measure theory. Solutions to all exercises are available to instructors who adopt the text for coursework. Most chapters use the same structure with the first part presenting theory and the next containing a healthy range of exercises. Some of the exercises may even be considered as short introductions to ideas which are not covered in the theory portion. Each chapter has a notes section offering a rich narrative to accompany the theory, illuminating the development of ideas, and providing overviews to the literature concerning the covered topics. In most cases, these notes bring the reader to the research front. The text includes many figures that illustrate concepts and some parts of the proofs, enabling the reader to have a better understanding of the geometric meaning of the ideas. An appendix containing basic (and geometric) measure theory collects useful information for convex geometers.
Convexity From The Geometric Point Of View Exercises And Solutions
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Author : Vitor Balestro
language : en
Publisher: Birkhäuser
Release Date : 2025-05-24
Convexity From The Geometric Point Of View Exercises And Solutions written by Vitor Balestro and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-24 with Mathematics categories.
This book provides the solutions to all 347 exercises contained in the text Convexity from the Geometric Point of View, published in the same Cornerstones series. All these exercises are restated and numbered analogously to those in the original text. The corresponding solutions follow each exercise. Besides the discussion of all solutions, some additional facts about the main text are sprinkled throughout. Sections of further reading are posted to the ends of each chapter supplying the reader with background literature to selected notions and tools that play a role in the exercises and/or solutions to the chapter. The original text gives a comprehensive introduction to the “common core” of convex geometry and is suitable as a primary text for courses in convex geometry and in discrete geometry (including polytopes). Additionally, it can be used as a single reference for a complete introduction to convex geometry. The content coverage is sufficiently broad that the reader may gain a glimpse of the entire breadth of the field, various subfields, and interesting connections to neighboring disciplines. Mainly directed to graduate and advanced undergraduates, the original text is self-contained in such a way that it can be read by anyone who has standard undergraduate knowledge of analysis and of linear algebra. The same is true for this book of solutions.
Convex Optimization
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Author : Stephen P. Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2004-03-08
Convex Optimization written by Stephen P. Boyd and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-08 with Business & Economics categories.
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.
Linear Problems And Convexity Techniques In Geometric Function Theory
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Author : David J. Hallenbeck
language : en
Publisher: Pitman Publishing
Release Date : 1984
Linear Problems And Convexity Techniques In Geometric Function Theory written by David J. Hallenbeck and has been published by Pitman Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
Geometric Problems On Maxima And Minima
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Author : Titu Andreescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-08
Geometric Problems On Maxima And Minima written by Titu Andreescu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-08 with Mathematics categories.
Presents hundreds of extreme value problems, examples, and solutions primarily through Euclidean geometry Unified approach to the subject, with emphasis on geometric, algebraic, analytic, and combinatorial reasoning Applications to physics, engineering, and economics Ideal for use at the junior and senior undergraduate level, with wide appeal to students, teachers, professional mathematicians, and puzzle enthusiasts
Semidefinite Optimization And Convex Algebraic Geometry
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Author : Grigoriy Blekherman
language : en
Publisher: SIAM
Release Date : 2013-03-21
Semidefinite Optimization And Convex Algebraic Geometry written by Grigoriy Blekherman and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-21 with Mathematics categories.
An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.
Choice
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Author : Richard K. Gardner
language : en
Publisher:
Release Date : 1976
Choice written by Richard K. Gardner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Best books categories.
Convex Optimization Theory
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Author : Dimitri P. Bertsekas
language : en
Publisher:
Release Date : 2010
Convex Optimization Theory written by Dimitri P. Bertsekas and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Convex functions categories.
Lectures On Convex Geometry
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Author : Daniel Hug
language : en
Publisher: Springer
Release Date : 2021-09-11
Lectures On Convex Geometry written by Daniel Hug and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-11 with Mathematics categories.
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.