undergraduate convexity from fourier and motzkin to kuhn and tucker

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Undergraduate Convexity

Author : Niels Lauritzen
ISBN : 9789814412537
Genre : Mathematics
File Size : 30. 81 MB
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Based on undergraduate teaching to students in computer science, economics and mathematics at Aarhus University, this is an elementary introduction to convex sets and convex functions with emphasis on concrete computations and examples. Starting from linear inequalities and Fourier–Motzkin elimination, the theory is developed by introducing polyhedra, the double description method and the simplex algorithm, closed convex subsets, convex functions of one and several variables ending with a chapter on convex optimization with the Karush–Kuhn–Tucker conditions, duality and an interior point algorithm. Contents:Fourier–Motzkin Elimination Affine SubspacesConvex SubsetsPolyhedraComputations with PolyhedraClosed Convex Subsets and Separating HyperplanesConvex FunctionsDifferentiable Functions of Several VariablesConvex Functions of Several VariablesConvex OptimizationAppendices:AnalysisLinear (In)dependence and the Rank of a Matrix Readership: Undergraduates focusing on convexity and optimization. Keywords:Convex Sets;Covex Functions;Fourier–Motzkin Eliminination;Karush–Kuhn–Tucker Conditions;Quadratic OptimizationKey Features:Emphasis on viewing introductory convexity as a generalization of linear algebra in finding solutions to linear inequalitiesA key point is computation through concrete algorithms like the double description method. This enables students to carry out non-trivial computations alongside the introduction of the mathematical conceptsConvexity is inherently a geometric subject. However, without computational techniques, the teaching of the subject turns easily into a reproduction of abstractions and definitions. The book addresses this issue at a basic levelReviews: “Overall, the author has managed to keep a sound balance between the different approaches to convexity in geometry, analysis, and applied mathematics. The entire presentation is utmost lucid, didactically well-composed, thematically versatile and essentially self-contained. The large number of instructive examples and illustrating figures will certainly help the unexperienced reader grasp the abstract concepts, methods and results, all of which are treated in a mathematically rigorous way. Also, the emphasis on computational, especially algorithmic methods is a particular feature of this fine undergraduate textbook, which will be a great source for students and instructors like-wise … the book under review is an excellent, rather unique primer on convexity in several branches of mathematics.” Zentralblatt MATH “Undergraduate Convexity would make an excellent textbook. An instructor might choose to have students present some of the examples while he or she provides commentary, perhaps alternating coaching and lecturing. A course taught from this book could be a good transition into more abstract mathematics, exposing students to general theory then giving them the familiar comfort of more computational exercises. One could also use the book as a warm-up to a more advanced course in optimization.” MAA Review “The book is didactically written in a pleasant and lively style, with careful motivation of the considered notions, illuminating examples and pictures, and relevant historical remarks. This is a remarkable book, a readable and attractive introduction to the multi-faceted domain of convexity and its applications.” Nicolae Popovici Stud. Univ. Babes-Bolyai Math “Compared to most modern undergraduate math textbooks, this book is unusually thin and portable. It also contains a wealth of material, presented in a concise and delightful way, accompanied by figures, historical references, pointers to further reading, pictures of great mathematicians and snapshots of pages of their groundbreaking papers. There are numerous exercises, both of computational and theoretical nature. If you want to teach an undergraduate convexity course, this looks like an excellent choice for the textbook.” MathSciNet

Undergraduate Convexity

Author : Mikkel Slot Nielsen
ISBN : 9789813143661
Genre : Mathematics
File Size : 75. 67 MB
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This solutions manual thoroughly goes through the exercises found in Undergraduate Convexity: From Fourier and Motzkin to Kuhn and Tucker. Several solutions are accompanied by detailed illustrations and intuitive explanations. This book will pave the way for students to easily grasp the multitude of solution methods and aspects of convex sets and convex functions. Request Inspection Copy

Convexity And Optimization In Rn

Author : Leonard D. Berkovitz
ISBN : 9780471461661
Genre : Mathematics
File Size : 30. 33 MB
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A comprehensive introduction to convexity and optimization in Rn This book presents the mathematics of finite dimensional constrained optimization problems. It provides a basis for the further mathematical study of convexity, of more general optimization problems, and of numerical algorithms for the solution of finite dimensional optimization problems. For readers who do not have the requisite background in real analysis, the author provides a chapter covering this material. The text features abundant exercises and problems designed to lead the reader to a fundamental understanding of the material. Convexity and Optimization in Rn provides detailed discussion of: * Requisite topics in real analysis * Convex sets * Convex functions * Optimization problems * Convex programming and duality * The simplex method A detailed bibliography is included for further study and an index offers quick reference. Suitable as a text for both graduate and undergraduate students in mathematics and engineering, this accessible text is written from extensively class-tested notes.

Matrix Computations

Author : Gene H. Golub
ISBN : 9781421407944
Genre : Mathematics
File Size : 29. 96 MB
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The fourth edition of Gene H. Golub and Charles F. Van Loan's classic is an essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this book to be an indispensible tool. This revision is a cover-to-cover expansion and renovation of the third edition. It now includes an introduction to tensor computations and brand new sections on • fast transforms• parallel LU• discrete Poisson solvers• pseudospectra• structured linear equation problems• structured eigenvalue problems• large-scale SVD methods• polynomial eigenvalue problems Matrix Computations is packed with challenging problems, insightful derivations, and pointers to the literature—everything needed to become a matrix-savvy developer of numerical methods and software.

Linear Programming And Network Flows

Author : Mokhtar S. Bazaraa
ISBN : 9780471703761
Genre : Mathematics
File Size : 52. 12 MB
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Understanding And Using Linear Programming

Author : Jiri Matousek
ISBN : 9783540307174
Genre : Mathematics
File Size : 78. 70 MB
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The book is an introductory textbook mainly for students of computer science and mathematics. Our guiding phrase is "what every theoretical computer scientist should know about linear programming". A major focus is on applications of linear programming, both in practice and in theory. The book is concise, but at the same time, the main results are covered with complete proofs and in sufficient detail, ready for presentation in class. The book does not require more prerequisites than basic linear algebra, which is summarized in an appendix. One of its main goals is to help the reader to see linear programming "behind the scenes".

Proofs From The Book

Author : Martin Aigner
ISBN : 9783662442050
Genre : Mathematics
File Size : 25. 55 MB
Format : PDF
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This revised and enlarged fifth edition features four new chapters, which contain highly original and delightful proofs for classics such as the spectral theorem from linear algebra, some more recent jewels like the non-existence of the Borromean rings and other surprises. From the Reviews "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..." LMS Newsletter, January 1999 "Martin Aigner and Günter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdös. The theorems are so fundamental, their proofs so elegant and the remaining open questio ns so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... " SIGACT News, December 2011.

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