Duality Principles In Nonconvex Systems
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Duality Principles In Nonconvex Systems
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Author : David Yang Gao
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-01-31
Duality Principles In Nonconvex Systems written by David Yang Gao 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 2000-01-31 with Mathematics categories.
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.
Duality Principles In Nonconvex Systems
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Author : David Yang Gao
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Duality Principles In Nonconvex Systems written by David Yang Gao 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 2013-03-09 with Mathematics categories.
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 alsobe 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.
Canonical Duality Theory
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Author : David Yang Gao
language : en
Publisher: Springer
Release Date : 2017-10-09
Canonical Duality Theory written by David Yang Gao and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-09 with Mathematics categories.
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.
Complementarity Duality And Symmetry In Nonlinear Mechanics
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Author : David Yang Gao
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-08
Complementarity Duality And Symmetry In Nonlinear Mechanics written by David Yang Gao 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 2012-11-08 with Technology & Engineering categories.
Complementarity, duality, and symmetry are closely related concepts, and have always been a rich source of inspiration in human understanding through the centuries, particularly in mathematics and science. The Proceedings of IUTAM Symposium on Complementarity, Duality, and Symmetry in Nonlinear Mechanics brings together some of world's leading researchers in both mathematics and mechanics to provide an interdisciplinary but engineering flavoured exploration of the field's foundation and state of the art developments. Topics addressed in this book deal with fundamental theory, methods, and applications of complementarity, duality and symmetry in multidisciplinary fields of nonlinear mechanics, including nonconvex and nonsmooth elasticity, dynamics, phase transitions, plastic limit and shakedown analysis of hardening materials and structures, bifurcation analysis, entropy optimization, free boundary value problems, minimax theory, fluid mechanics, periodic soliton resonance, constrained mechanical systems, finite element methods and computational mechanics. A special invited paper presented important research opportunities and challenges of the theoretical and applied mechanics as well as engineering materials in the exciting information age. Audience: This book is addressed to all scientists, physicists, engineers and mathematicians, as well as advanced students (doctoral and post-doctoral level) at universities and in industry.
Optimization And Optimal Control
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Author : Altannar Chinchuluun
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-05
Optimization And Optimal Control written by Altannar Chinchuluun 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 2010-08-05 with Mathematics categories.
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.
Encyclopedia Of Optimization
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Author : Christodoulos A. Floudas
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-04
Encyclopedia Of Optimization written by Christodoulos A. Floudas 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 2008-09-04 with Mathematics categories.
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".
Advances In Mechanics And Mathematics
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Author : David Yang Gao
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Advances In Mechanics And Mathematics written by David Yang Gao 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 2013-12-01 with Science categories.
As any human activity needs goals, mathematical research needs problems -David Hilbert Mechanics is the paradise of mathematical sciences -Leonardo da Vinci Mechanics and mathematics have been complementary partners since Newton's time and the history of science shows much evidence of the ben eficial influence of these disciplines on each other. Driven by increasingly elaborate modern technological applications the symbiotic relationship between mathematics and mechanics is continually growing. However, the increasingly large number of specialist journals has generated a du ality gap between the two partners, and this gap is growing wider. Advances in Mechanics and Mathematics (AMMA) is intended to bridge the gap by providing multi-disciplinary publications which fall into the two following complementary categories: 1. An annual book dedicated to the latest developments in mechanics and mathematics; 2. Monographs, advanced textbooks, handbooks, edited vol umes and selected conference proceedings. The AMMA annual book publishes invited and contributed compre hensive reviews, research and survey articles within the broad area of modern mechanics and applied mathematics. Mechanics is understood here in the most general sense of the word, and is taken to embrace relevant physical and biological phenomena involving electromagnetic, thermal and quantum effects and biomechanics, as well as general dy namical systems. Especially encouraged are articles on mathematical and computational models and methods based on mechanics and their interactions with other fields. All contributions will be reviewed so as to guarantee the highest possible scientific standards.
Advances In Global Optimization
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Author : David Gao
language : en
Publisher: Springer
Release Date : 2014-11-11
Advances In Global Optimization written by David Gao and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-11 with Mathematics categories.
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.
Neural Information Processing
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Author : Tingwen Huang
language : en
Publisher: Springer
Release Date : 2012-11-05
Neural Information Processing written by Tingwen Huang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-05 with Computers categories.
The five volume set LNCS 7663, LNCS 7664, LNCS 7665, LNCS 7666 and LNCS 7667 constitutes the proceedings of the 19th International Conference on Neural Information Processing, ICONIP 2012, held in Doha, Qatar, in November 2012. The 423 regular session papers presented were carefully reviewed and selected from numerous submissions. These papers cover all major topics of theoretical research, empirical study and applications of neural information processing research. The 5 volumes represent 5 topical sections containing articles on theoretical analysis, neural modeling, algorithms, applications, as well as simulation and synthesis.
Global Optimization With Non Convex Constraints
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Author : Roman G. Strongin
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-10-31
Global Optimization With Non Convex Constraints written by Roman G. Strongin 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 2000-10-31 with Computers categories.
This book presents a new approach to global non-convex constrained optimization. Problem dimensionality is reduced via space-filling curves. To economize the search, constraint is accounted separately (penalties are not employed). The multicriteria case is also considered. All techniques are generalized for (non-redundant) execution on multiprocessor systems. Audience: Researchers and students working in optimization, applied mathematics, and computer science.