Cones And Duality

Author : Charalambos D. Aliprantis,Rabee Tourky
Publisher : American Mathematical Soc.
Page : 298 pages
File Size : 52,8 Mb
Release : 2007-06-12
Category : Mathematics
ISBN : 9780821841464

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Cones and Duality by Charalambos D. Aliprantis,Rabee Tourky Pdf

Ordered vector spaces and cones made their debut in mathematics at the beginning of the twentieth century. They were developed in parallel (but from a different perspective) with functional analysis and operator theory. Before the 1950s, ordered vector spaces appeared in the literature in a fragmented way. Their systematic study began around the world after 1950 mainly through the efforts of the Russian, Japanese, German, and Dutch schools. Since cones are being employed to solve optimization problems, the theory of ordered vector spaces is an indispensable tool for solving a variety of applied problems appearing in several diverse areas, such as engineering, econometrics, and the social sciences. For this reason this theory plays a prominent role not only in functional analysis but also in a wide range of applications. This is a book about a modern perspective on cones and ordered vector spaces. It includes material that has not been presented earlier in a monograph or a textbook. With many exercises of varying degrees of difficulty, the book is suitable for graduate courses. Most of the new topics currently discussed in the book have their origins in problems from economics and finance. Therefore, the book will be valuable to any researcher and graduate student who works in mathematics, engineering, economics, finance, and any other field that uses optimization techniques.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 47,8 Mb
Release : 2024-07-03
Category : Electronic
ISBN : OCLC:236021308

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الياس أبو شيكة by Anonim Pdf

Author : Rolf Schneider
Publisher : Springer Nature
Page : 352 pages
File Size : 48,9 Mb
Release : 2022-09-21
Category : Mathematics
ISBN : 9783031151279

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Convex Cones by Rolf Schneider Pdf

This book provides the foundations for geometric applications of convex cones and presents selected examples from a wide range of topics, including polytope theory, stochastic geometry, and Brunn–Minkowski theory. Giving an introduction to convex cones, it describes their most important geometric functionals, such as conic intrinsic volumes and Grassmann angles, and develops general versions of the relevant formulas, namely the Steiner formula and kinematic formula. In recent years questions related to convex cones have arisen in applied mathematics, involving, for example, properties of random cones and their non-trivial intersections. The prerequisites for this work, such as integral geometric formulas and results on conic intrinsic volumes, were previously scattered throughout the literature, but no coherent presentation was available. The present book closes this gap. It includes several pearls from the theory of convex cones, which should be better known.

Author : Jan Brinkhuis
Publisher : Springer Nature
Page : 278 pages
File Size : 47,5 Mb
Release : 2020-05-05
Category : Business & Economics
ISBN : 9783030418045

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Convex Analysis for Optimization by Jan Brinkhuis Pdf

This textbook offers graduate students a concise introduction to the classic notions of convex optimization. Written in a highly accessible style and including numerous examples and illustrations, it presents everything readers need to know about convexity and convex optimization. The book introduces a systematic three-step method for doing everything, which can be summarized as "conify, work, deconify". It starts with the concept of convex sets, their primal description, constructions, topological properties and dual description, and then moves on to convex functions and the fundamental principles of convex optimization and their use in the complete analysis of convex optimization problems by means of a systematic four-step method. Lastly, it includes chapters on alternative formulations of optimality conditions and on illustrations of their use. "The author deals with the delicate subjects in a precise yet light-minded spirit... For experts in the field, this book not only offers a unifying view, but also opens a door to new discoveries in convexity and optimization...perfectly suited for classroom teaching." Shuzhong Zhang, Professor of Industrial and Systems Engineering, University of Minnesota

Author : Klaus Keimel,Walter Roth
Publisher : Springer
Page : 140 pages
File Size : 44,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540470793

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Ordered Cones and Approximation by Klaus Keimel,Walter Roth Pdf

This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.

Author : Mikhail J. Atallah,Marina Blanton
Publisher : CRC Press
Page : 1944 pages
File Size : 53,8 Mb
Release : 2022-05-30
Category : Computers
ISBN : 9781439832332

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Algorithms and Theory of Computation Handbook - 2 Volume Set by Mikhail J. Atallah,Marina Blanton Pdf

Algorithms and Theory of Computation Handbook, Second Edition in a two volume set, provides an up-to-date compendium of fundamental computer science topics and techniques. It also illustrates how the topics and techniques come together to deliver efficient solutions to important practical problems. New to the Second Edition: Along with updating and revising many of the existing chapters, this second edition contains more than 20 new chapters. This edition now covers external memory, parameterized, self-stabilizing, and pricing algorithms as well as the theories of algorithmic coding, privacy and anonymity, databases, computational games, and communication networks. It also discusses computational topology, computational number theory, natural language processing, and grid computing and explores applications in intensity-modulated radiation therapy, voting, DNA research, systems biology, and financial derivatives. This best-selling handbook continues to help computer professionals and engineers find significant information on various algorithmic topics. The expert contributors clearly define the terminology, present basic results and techniques, and offer a number of current references to the in-depth literature. They also provide a glimpse of the major research issues concerning the relevant topics

Author : Mikhail J. Atallah,Marina Blanton
Publisher : CRC Press
Page : 974 pages
File Size : 48,6 Mb
Release : 2009-11-20
Category : Computers
ISBN : 9781584888239

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Algorithms and Theory of Computation Handbook, Volume 1 by Mikhail J. Atallah,Marina Blanton Pdf

Algorithms and Theory of Computation Handbook, Second Edition: General Concepts and Techniques provides an up-to-date compendium of fundamental computer science topics and techniques. It also illustrates how the topics and techniques come together to deliver efficient solutions to important practical problems. Along with updating and revising many

Author : Yoshihiro Kanno
Publisher : CRC Press
Page : 447 pages
File Size : 55,8 Mb
Release : 2011-04-05
Category : Science
ISBN : 9781420094237

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Nonsmooth Mechanics and Convex Optimization by Yoshihiro Kanno Pdf

"This book concerns matter that is intrinsically difficult: convex optimization, complementarity and duality, nonsmooth analysis, linear and nonlinear programming, etc. The author has skillfully introduced these and many more concepts, and woven them into a seamless whole by retaining an easy and consistent style throughout. The book is not all theory: There are many real-life applications in structural engineering, cable networks, frictional contact problems, and plasticity... I recommend it to any reader who desires a modern, authoritative account of nonsmooth mechanics and convex optimization." — Prof. Graham M.L. Gladwell, Distinguished Professor Emeritus, University of Waterloo, Fellow of the Royal Society of Canada "... reads very well—the structure is good, the language and style are clear and fluent, and the material is rendered accessible by a careful presentation that contains many concrete examples. The range of applications, particularly to problems in mechanics, is admirable and a valuable complement to theoretical and computational investigations that are at the forefront of the areas concerned." — Prof. B. Daya Reddy, Department of Mathematics and Applied Mathematics, Director of Centre for Research in Computational and Applied Mechanics, University of Cape Town, South Africa "Many materials and structures (e.g., cable networks, membrane) involved in practical engineering applications have complex responses that cannot be described by smooth constitutive relations. ... The author shows how these difficult problems can be tackled in the framework of convex analysis by arranging the carefully chosen materials in an elegant way. Most of the contents of the book are from the original contributions of the author. They are both mathematically rigorous and readable. This book is a must-read for anyone who intends to get an authoritative and state-of-art description for the analysis of nonsmooth mechanics problems with theory and tools from convex analysis." — Prof. Xu Guo, State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology

Author : Elon Rimon,Joel Burdick
Publisher : Cambridge University Press
Page : 509 pages
File Size : 44,9 Mb
Release : 2019-10-24
Category : Computers
ISBN : 9781108427906

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The Mechanics of Robot Grasping by Elon Rimon,Joel Burdick Pdf

This comprehensive look at the major concepts in robot grasp mechanics serves as a valuable reference for all robotics enthusiasts.

Author : Alfred Auslender,Marc Teboulle
Publisher : Springer Science & Business Media
Page : 259 pages
File Size : 43,5 Mb
Release : 2006-05-07
Category : Mathematics
ISBN : 9780387225906

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Asymptotic Cones and Functions in Optimization and Variational Inequalities by Alfred Auslender,Marc Teboulle Pdf

This systematic and comprehensive account of asymptotic sets and functions develops a broad and useful theory in the areas of optimization and variational inequalities. The central focus is on problems of handling unbounded situations, using solutions of a given problem in these classes, when for example standard compacity hypothesis is not present. This book will interest advanced graduate students, researchers, and practitioners of optimization theory, nonlinear programming, and applied mathematics.

Author : Javier Esparza,Andrzej S. Murawski
Publisher : Springer
Page : 568 pages
File Size : 43,5 Mb
Release : 2017-03-15
Category : Computers
ISBN : 9783662544587

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Foundations of Software Science and Computation Structures by Javier Esparza,Andrzej S. Murawski Pdf

This book constitutes the proceedings of the 20th International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2017, which took place in Uppsala, Sweden in April 2017, held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017. The 32 papers presented in this volume were carefully reviewed and selected from 101 submissions. They were organized in topical sections named: coherence spaces and higher-order computation; algebra and coalgebra; games and automata; automata, logic and formal languages; proof theory; probability; concurrency; lambda calculus and constructive proof; and semantics and category theory.

Author : Guillaume Aubrun,Stanisław J. Szarek
Publisher : American Mathematical Soc.
Page : 414 pages
File Size : 46,9 Mb
Release : 2017-08-30
Category : Functional analysis
ISBN : 9781470434687

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Alice and Bob Meet Banach: The Interface of Asymptotic Geometric Analysis and Quantum Information Theory by Guillaume Aubrun,Stanisław J. Szarek Pdf

The quest to build a quantum computer is arguably one of the major scientific and technological challenges of the twenty-first century, and quantum information theory (QIT) provides the mathematical framework for that quest. Over the last dozen or so years, it has become clear that quantum information theory is closely linked to geometric functional analysis (Banach space theory, operator spaces, high-dimensional probability), a field also known as asymptotic geometric analysis (AGA). In a nutshell, asymptotic geometric analysis investigates quantitative properties of convex sets, or other geometric structures, and their approximate symmetries as the dimension becomes large. This makes it especially relevant to quantum theory, where systems consisting of just a few particles naturally lead to models whose dimension is in the thousands, or even in the billions. Alice and Bob Meet Banach is aimed at multiple audiences connected through their interest in the interface of QIT and AGA: at quantum information researchers who want to learn AGA or apply its tools; at mathematicians interested in learning QIT, or at least the part of QIT that is relevant to functional analysis/convex geometry/random matrix theory and related areas; and at beginning researchers in either field. Moreover, this user-friendly book contains numerous tables and explicit estimates, with reasonable constants when possible, which make it a useful reference even for established mathematicians generally familiar with the subject.

Author : Alexandre V. Borovik,Anna Borovik
Publisher : Springer Science & Business Media
Page : 172 pages
File Size : 47,5 Mb
Release : 2009-11-07
Category : Mathematics
ISBN : 9780387790664

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Mirrors and Reflections by Alexandre V. Borovik,Anna Borovik Pdf

This graduate/advanced undergraduate textbook contains a systematic and elementary treatment of finite groups generated by reflections. The approach is based on fundamental geometric considerations in Coxeter complexes, and emphasizes the intuitive geometric aspects of the theory of reflection groups. Key features include: many important concepts in the proofs are illustrated in simple drawings, which give easy access to the theory; a large number of exercises at various levels of difficulty; some Euclidean geometry is included along with the theory of convex polyhedra; no prerequisites are necessary beyond the basic concepts of linear algebra and group theory; and a good index and bibliography The exposition is directed at advanced undergraduates and first-year graduate students.

Author : B. Rushi Kumar,S. Ponnusamy,Debasis Giri,Bhavani Thuraisingham,Christopher W. Clifton,Barbara Carminati
Publisher : Springer Nature
Page : 701 pages
File Size : 53,9 Mb
Release : 2023-03-14
Category : Mathematics
ISBN : 9789811993077

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Mathematics and Computing by B. Rushi Kumar,S. Ponnusamy,Debasis Giri,Bhavani Thuraisingham,Christopher W. Clifton,Barbara Carminati Pdf

This book comprises select peer-reviewed articles submitted for the proceedings of the International Conference on Mathematics and Computing (ICMC 2022), held by the School of Advanced Sciences, Vellore Institute of Technology, Vellore, India, in association with Ramanujan Mathematical Society, India, Cryptology Research Society of India and Society for Electronic Transactions and Security, India, from 6–8 January 2022. With an aim to identify the existing challenges in the areas of mathematics and computing, the book emphasizes the importance of establishing new methods and algorithms to address these challenges. The book includes topics on diverse applications of cryptology, network security, cyber security, block chain, IoT, mobile network, data analytics, applied algebra, mathematical analysis, mathematical modelling, fluid dynamics, fractional calculus, multi-optimization, integral equations, dynamical systems, numerical analysis and scientific computing. Divided into five major parts—applied algebra and analysis, fractional calculus and integral equations, mathematical modelling and fluid dynamics, numerical analysis, and computer science and applications—the book is a useful resource for students, researchers and faculty as well as practitioners.

Author : Jonathan Borwein,Adrian S. Lewis
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 48,8 Mb
Release : 2010-05-05
Category : Mathematics
ISBN : 9780387312569

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Convex Analysis and Nonlinear Optimization by Jonathan Borwein,Adrian S. Lewis Pdf

Optimization is a rich and thriving mathematical discipline, and the underlying theory of current computational optimization techniques grows ever more sophisticated. This book aims to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. Each section concludes with an often extensive set of optional exercises. This new edition adds material on semismooth optimization, as well as several new proofs.