Canonical Duality Theory

Author : David Yang Gao,Vittorio Latorre,Ning Ruan
Publisher : Springer
Page : 377 pages
File Size : 49,8 Mb
Release : 2017-10-09
Category : Mathematics
ISBN : 9783319580173

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Canonical Duality Theory by David Yang Gao,Vittorio Latorre,Ning Ruan Pdf

This book on canonical duality theory provides a comprehensive review of its philosophical origin, physics foundation, and mathematical statements in both finite- and infinite-dimensional spaces. A ground-breaking methodological theory, canonical duality theory can be used for modeling complex systems within a unified framework and for solving a large class of challenging problems in multidisciplinary fields in engineering, mathematics, and the sciences. This volume places a particular emphasis on canonical duality theory’s role in bridging the gap between non-convex analysis/mechanics and global optimization. With 18 total chapters written by experts in their fields, this volume provides a nonconventional theory for unified understanding of the fundamental difficulties in large deformation mechanics, bifurcation/chaos in nonlinear science, and the NP-hard problems in global optimization. Additionally, readers will find a unified methodology and powerful algorithms for solving challenging problems in complex systems with real-world applications in non-convex analysis, non-monotone variational inequalities, integer programming, topology optimization, post-buckling of large deformed structures, etc. Researchers and graduate students will find explanation and potential applications in multidisciplinary fields.

Author : David Yang Gao
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 50,6 Mb
Release : 2000-01-31
Category : Mathematics
ISBN : 0792361458

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Duality Principles in Nonconvex Systems by David Yang Gao Pdf

Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems. With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis. Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed.

Author : David Yang Gao
Publisher : Springer Science & Business Media
Page : 463 pages
File Size : 52,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475731767

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Duality Principles in Nonconvex Systems by David Yang Gao Pdf

Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems. With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis. Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed.

Author : Allen Altman,Steven Kleiman
Publisher : Springer
Page : 188 pages
File Size : 47,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540363095

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Introduction to Grothendieck Duality Theory by Allen Altman,Steven Kleiman Pdf

Author : Yaroslav D. Sergeyev,Dmitri E. Kvasov,Francesco Dell'Accio
Publisher : Luigi Pellegrini Editore
Page : 152 pages
File Size : 42,8 Mb
Release : 2013-06-27
Category : Mathematics
ISBN : 9788868220334

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Proceedings of the international conference "“NUMERICAL COMPUTATIONS: THEORY AND ALGORITHMS” by Yaroslav D. Sergeyev,Dmitri E. Kvasov,Francesco Dell'Accio Pdf

This book contains Proceedings of the International Conference and Summer School NUMTA-2013 “Numerical Computations: Theory and Algorithms”. The Conference is organized jointly by the University of Calabria, Italy, and by the N.I. Lobachevsky State University of Nizhni Novgorod, Russia in cooperation with the Society for Industrial and Applied Mathematics (SIAM), USA. The goal of the Conference is to create a multidisciplinary round table for an open discussion on numerical modeling nature by using traditional and emerging computational paradigms. The Conference discusses all aspects of numerical computations and modeling from foundations and philosophy to advanced numerical techniques. New technological challenges and fundamental ideas from theoretical computer science, linguistic, logic, set theory, and philosophy meet requirements and new fresh applications from physics, chemistry, biology, and economy.

Author : Vinai K. Singh,David Gao,Andreas Fischer
Publisher : Springer
Page : 503 pages
File Size : 40,7 Mb
Release : 2019-02-14
Category : Computers
ISBN : 9783030024871

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Advances in Mathematical Methods and High Performance Computing by Vinai K. Singh,David Gao,Andreas Fischer Pdf

This special volume of the conference will be of immense use to the researchers and academicians. In this conference, academicians, technocrats and researchers will get an opportunity to interact with eminent persons in the field of Applied Mathematics and Scientific Computing. The topics to be covered in this International Conference are comprehensive and will be adequate for developing and understanding about new developments and emerging trends in this area. High-Performance Computing (HPC) systems have gone through many changes during the past two decades in their architectural design to satisfy the increasingly large-scale scientific computing demand. Accurate, fast, and scalable performance models and simulation tools are essential for evaluating alternative architecture design decisions for the massive-scale computing systems. This conference recounts some of the influential work in modeling and simulation for HPC systems and applications, identifies some of the major challenges, and outlines future research directions which we believe are critical to the HPC modeling and simulation community.

Author : Hoai An Le Thi,Hoai Minh Le,Tao Pham Dinh
Publisher : Springer
Page : 1164 pages
File Size : 42,5 Mb
Release : 2019-06-15
Category : Technology & Engineering
ISBN : 9783030218034

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Optimization of Complex Systems: Theory, Models, Algorithms and Applications by Hoai An Le Thi,Hoai Minh Le,Tao Pham Dinh Pdf

This book contains 112 papers selected from about 250 submissions to the 6th World Congress on Global Optimization (WCGO 2019) which takes place on July 8–10, 2019 at University of Lorraine, Metz, France. The book covers both theoretical and algorithmic aspects of Nonconvex Optimization, as well as its applications to modeling and solving decision problems in various domains. It is composed of 10 parts, each of them deals with either the theory and/or methods in a branch of optimization such as Continuous optimization, DC Programming and DCA, Discrete optimization & Network optimization, Multiobjective programming, Optimization under uncertainty, or models and optimization methods in a specific application area including Data science, Economics & Finance, Energy & Water management, Engineering systems, Transportation, Logistics, Resource allocation & Production management. The researchers and practitioners working in Nonconvex Optimization and several application areas can find here many inspiring ideas and useful tools & techniques for their works.

Author : J. S. Milne
Publisher : Unknown
Page : 440 pages
File Size : 41,8 Mb
Release : 1986
Category : Mathematics
ISBN : UOM:39076000806617

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Arithmetic Duality Theorems by J. S. Milne Pdf

Here, published for the first time, are the complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry. The text covers these theorems in Galois cohomology, ,tale cohomology, and flat cohomology and addresses applications in the above areas. The writing is expository and the book will serve as an invaluable reference text as well as an excellent introduction to the subject.

Author : David Gao,Ning Ruan,Wenxun Xing
Publisher : Springer
Page : 537 pages
File Size : 52,5 Mb
Release : 2014-11-11
Category : Mathematics
ISBN : 9783319083773

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Advances in Global Optimization by David Gao,Ning Ruan,Wenxun Xing Pdf

This proceedings volume addresses advances in global optimization—a multidisciplinary research field that deals with the analysis, characterization and computation of global minima and/or maxima of nonlinear, non-convex and nonsmooth functions in continuous or discrete forms. The volume contains selected papers from the third biannual World Congress on Global Optimization in Engineering & Science (WCGO), held in the Yellow Mountains, Anhui, China on July 8-12, 2013. The papers fall into eight topical sections: mathematical programming; combinatorial optimization; duality theory; topology optimization; variational inequalities and complementarity problems; numerical optimization; stochastic models and simulation and complex simulation and supply chain analysis.

Author : David Y. Gao,Hanif D. Sherali
Publisher : Springer Science & Business Media
Page : 520 pages
File Size : 52,9 Mb
Release : 2009-04-09
Category : Mathematics
ISBN : 9780387757148

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Advances in Applied Mathematics and Global Optimization by David Y. Gao,Hanif D. Sherali Pdf

The articles that comprise this distinguished annual volume for the Advances in Mechanics and Mathematics series have been written in honor of Gilbert Strang, a world renowned mathematician and exceptional person. Written by leading experts in complementarity, duality, global optimization, and quantum computations, this collection reveals the beauty of these mathematical disciplines and investigates recent developments in global optimization, nonconvex and nonsmooth analysis, nonlinear programming, theoretical and engineering mechanics, large scale computation, quantum algorithms and computation, and information theory.

Author : Guram Bezhanishvili
Publisher : Springer
Page : 334 pages
File Size : 46,5 Mb
Release : 2014-06-03
Category : Philosophy
ISBN : 9789401788601

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Leo Esakia on Duality in Modal and Intuitionistic Logics by Guram Bezhanishvili Pdf

This volume is dedicated to Leo Esakia's contributions to the theory of modal and intuitionistic systems. Consisting of 10 chapters, written by leading experts, this volume discusses Esakia’s original contributions and consequent developments that have helped to shape duality theory for modal and intuitionistic logics and to utilize it to obtain some major results in the area. Beginning with a chapter which explores Esakia duality for S4-algebras, the volume goes on to explore Esakia duality for Heyting algebras and its generalizations to weak Heyting algebras and implicative semilattices. The book also dives into the Blok-Esakia theorem and provides an outline of the intuitionistic modal logic KM which is closely related to the Gödel-Löb provability logic GL. One chapter scrutinizes Esakia’s work interpreting modal diamond as the derivative of a topological space within the setting of point-free topology. The final chapter in the volume is dedicated to the derivational semantics of modal logic and other related issues.

Author : Altannar Chinchuluun,Panos M. Pardalos,Rentsen Enkhbat,Ider Tseveendorj
Publisher : Springer Science & Business Media
Page : 508 pages
File Size : 48,6 Mb
Release : 2010-07-07
Category : Mathematics
ISBN : 9780387894959

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Optimization and Optimal Control by Altannar Chinchuluun,Panos M. Pardalos,Rentsen Enkhbat,Ider Tseveendorj Pdf

Optimization and optimal control are the main tools in decision making. Because of their numerous applications in various disciplines, research in these areas is accelerating at a rapid pace. “Optimization and Optimal Control: Theory and Applications” brings together the latest developments in these areas of research as well as presents applications of these results to a wide range of real-world problems. This volume can serve as a useful resource for researchers, practitioners, and advanced graduate students of mathematics and engineering working in research areas where results in optimization and optimal control can be applied.

Author : Christodoulos A. Floudas,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 4646 pages
File Size : 44,9 Mb
Release : 2008-09-04
Category : Mathematics
ISBN : 9780387747583

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Encyclopedia of Optimization by Christodoulos A. Floudas,Panos M. Pardalos Pdf

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Author : Vladimir L. Boginski,Clayton W. Commander,Panos M. Pardalos,Yinyu Ye
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 54,8 Mb
Release : 2011-11-24
Category : Mathematics
ISBN : 9780387886190

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Sensors: Theory, Algorithms, and Applications by Vladimir L. Boginski,Clayton W. Commander,Panos M. Pardalos,Yinyu Ye Pdf

The objective of this book is to advance the current knowledge of sensor research particularly highlighting recent advances, current work, and future needs. The goal is to share current technologies and steer future efforts in directions that will benefit the majority of researchers and practitioners working in this broad field of study.

Author : Leo Esakia
Publisher : Springer
Page : 95 pages
File Size : 43,6 Mb
Release : 2019-07-05
Category : Philosophy
ISBN : 9783030120962

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Heyting Algebras by Leo Esakia Pdf

This book presents an English translation of a classic Russian text on duality theory for Heyting algebras. Written by Georgian mathematician Leo Esakia, the text proved popular among Russian-speaking logicians. This translation helps make the ideas accessible to a wider audience and pays tribute to an influential mind in mathematical logic. The book discusses the theory of Heyting algebras and closure algebras, as well as the corresponding intuitionistic and modal logics. The author introduces the key notion of a hybrid that “crossbreeds” topology (Stone spaces) and order (Kripke frames), resulting in the structures now known as Esakia spaces. The main theorems include a duality between the categories of closure algebras and of hybrids, and a duality between the categories of Heyting algebras and of so-called strict hybrids. Esakia’s book was originally published in 1985. It was the first of a planned two-volume monograph on Heyting algebras. But after the collapse of the Soviet Union, the publishing house closed and the project died with it. Fortunately, this important work now lives on in this accessible translation. The Appendix of the book discusses the planned contents of the lost second volume.