Duality Principles In Nonconvex Systems

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Duality Principles in Nonconvex Systems

David Yang Gao
Duality Principles in Nonconvex Systems Book PDF

Author : David Yang Gao
Publisher : Springer Science & Business Media
Page : 463 pages
File Size : 55,6 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.

Canonical Duality Theory

David Yang Gao,Vittorio Latorre,Ning Ruan
Canonical Duality Theory Book PDF

Author : David Yang Gao,Vittorio Latorre,Ning Ruan
Publisher : Springer
Page : 377 pages
File Size : 50,5 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.

Duality for Nonconvex Approximation and Optimization

Ivan Singer
Duality for Nonconvex Approximation and Optimization Book PDF

Author : Ivan Singer
Publisher : Springer Science & Business Media
Page : 366 pages
File Size : 49,6 Mb
Release : 2007-03-12
Category : Mathematics
ISBN : 9780387283951

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Duality for Nonconvex Approximation and Optimization by Ivan Singer Pdf

The theory of convex optimization has been constantly developing over the past 30 years. Most recently, many researchers have been studying more complicated classes of problems that still can be studied by means of convex analysis, so-called "anticonvex" and "convex-anticonvex" optimizaton problems. This manuscript contains an exhaustive presentation of the duality for these classes of problems and some of its generalization in the framework of abstract convexity. This manuscript will be of great interest for experts in this and related fields.

Control Of Nonlinear Distributed Parameter Systems

Goong Chen,Irena Lasiecka,Jianxin Zhou
Control Of Nonlinear Distributed Parameter Systems Book PDF

Author : Goong Chen,Irena Lasiecka,Jianxin Zhou
Publisher : CRC Press
Page : 380 pages
File Size : 40,6 Mb
Release : 2001-03-14
Category : Mathematics
ISBN : 9780824745059

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Control Of Nonlinear Distributed Parameter Systems by Goong Chen,Irena Lasiecka,Jianxin Zhou Pdf

An examination of progress in mathematical control theory applications. It provides analyses of the influence and relationship of nonlinear partial differential equations to control systems and contains state-of-the-art reviews, including presentations from a conference co-sponsored by the National Science Foundation, the Institute of Mathematics and its Applications, the University of Minnesota, and Texas A&M University.

Nonsmooth/Nonconvex Mechanics

David Yang Gao,Raymond W. Ogden,Georgios E. Stavroulakis
Nonsmooth Nonconvex Mechanics Book PDF

Author : David Yang Gao,Raymond W. Ogden,Georgios E. Stavroulakis
Publisher : Springer Science & Business Media
Page : 505 pages
File Size : 41,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461302759

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Nonsmooth/Nonconvex Mechanics by David Yang Gao,Raymond W. Ogden,Georgios E. Stavroulakis Pdf

Nonsmooth and nonconvex models arise in several important applications of mechanics and engineering. The interest in this field is growing from both mathematicians and engineers. The study of numerous industrial applications, including contact phenomena in statics and dynamics or delamination effects in composites, require the consideration of nonsmoothness and nonconvexity. The mathematical topics discussed in this book include variational and hemivariational inequalities, duality, complementarity, variational principles, sensitivity analysis, eigenvalue and resonance problems, and minimax problems. Applications are considered in the following areas among others: nonsmooth statics and dynamics, stability of quasi- static evolution processes, friction problems, adhesive contact and debonding, inverse problems, pseudoelastic modeling of phase transitions, chaotic behavior in nonlinear beams, and nonholonomic mechanical systems. This volume contains 22 chapters written by various leading researchers and presents a cohesive and authoritative overview of recent results and applications in the area of nonsmooth and nonconvex mechanics. Audience: Faculty, graduate students, and researchers in applied mathematics, optimization, control and engineering.

Advances in Applied Mathematics and Global Optimization

David Y. Gao,Hanif D. Sherali
Advances in Applied Mathematics and Global Optimization Book PDF

Author : David Y. Gao,Hanif D. Sherali
Publisher : Springer Science & Business Media
Page : 520 pages
File Size : 43,8 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.

From Convexity to Nonconvexity

R.P. Gilbert,Panagiotis D. Panagiotopoulos,Panos M. Pardalos
From Convexity to Nonconvexity Book PDF

Author : R.P. Gilbert,Panagiotis D. Panagiotopoulos,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 395 pages
File Size : 42,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461302872

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From Convexity to Nonconvexity by R.P. Gilbert,Panagiotis D. Panagiotopoulos,Panos M. Pardalos Pdf

This collection of papers is dedicated to the memory of Gaetano Fichera, a great mathematician and also a good friend to the editors. Regrettably it took an unusual amount of time to bring this collection out. This was primarily due to the fact that the main editor who had collected all of the materials, for this volume, P. D. Panagiotopoulos, died unexpectedly during the period when we were editing the manuscript. The other two editors in appreciation of Panagiotopoulos' contribution to this field, believe it is therefore fitting that this collection be dedicated to his memory also. The theme of the collection is centered around the seminal research of G. Fichera on the Signorini problem. Variants on this idea enter in different ways. For example, by bringing in friction the problem is no longer self-adjoint and the minimization formulation is not valid. A large portion of this collection is devoted to survey papers concerning hemivariational methods, with a main point of its application to nonsmooth mechanics. Hemivariational inequali ties, which are a generalization of variational inequalities, were pioneered by Panagiotopoulos. There are many applications of this theory to the study of non convex energy functionals occurring in many branches of mechanics. An area of concentration concerns contact problems, in particular, quasistatic and dynamic contact problems with friction and damage. Nonsmooth optimization methods which may be divided into the main groups of subgradient methods and bundle methods are also discussed in this collection.

Advances in Mathematical Methods and High Performance Computing

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

Author : Vinai K. Singh,David Gao,Andreas Fischer
Publisher : Springer
Page : 503 pages
File Size : 41,8 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.

Sensors: Theory, Algorithms, and Applications

Vladimir L. Boginski,Clayton W. Commander,Panos M. Pardalos,Yinyu Ye
Sensors Theory Algorithms and Applications Book PDF

Author : Vladimir L. Boginski,Clayton W. Commander,Panos M. Pardalos,Yinyu Ye
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 52,5 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.

Complementarity, Duality and Symmetry in Nonlinear Mechanics

David Yang Gao
Complementarity Duality and Symmetry in Nonlinear Mechanics Book PDF

Author : David Yang Gao
Publisher : Springer Science & Business Media
Page : 429 pages
File Size : 47,6 Mb
Release : 2012-11-08
Category : Technology & Engineering
ISBN : 9789048195770

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Complementarity, Duality and Symmetry in Nonlinear Mechanics by David Yang Gao Pdf

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.

Encyclopedia of Optimization

Christodoulos A. Floudas,Panos M. Pardalos
Encyclopedia of Optimization Book PDF

Author : Christodoulos A. Floudas,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 4646 pages
File Size : 43,5 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".

Optimization and Optimal Control

Altannar Chinchuluun,Panos M. Pardalos,Rentsen Enkhbat,Ider Tseveendorj
Optimization and Optimal Control Book PDF

Author : Altannar Chinchuluun,Panos M. Pardalos,Rentsen Enkhbat,Ider Tseveendorj
Publisher : Springer Science & Business Media
Page : 508 pages
File Size : 46,8 Mb
Release : 2010-08-05
Category : Mathematics
ISBN : 9780387894966

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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.

Neural Information Processing

Tingwen Huang,Zhigang Zeng,Chuandong Li,Chi-Sing Leung
Neural Information Processing Book PDF

Author : Tingwen Huang,Zhigang Zeng,Chuandong Li,Chi-Sing Leung
Publisher : Springer
Page : 740 pages
File Size : 52,6 Mb
Release : 2012-11-05
Category : Computers
ISBN : 9783642344879

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Neural Information Processing by Tingwen Huang,Zhigang Zeng,Chuandong Li,Chi-Sing Leung Pdf

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.

Advances in Global Optimization

David Gao,Ning Ruan,Wenxun Xing
Advances in Global Optimization Book PDF

Author : David Gao,Ning Ruan,Wenxun Xing
Publisher : Springer
Page : 522 pages
File Size : 50,6 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.

Global Optimization with Non-Convex Constraints

Roman G. Strongin,Yaroslav D. Sergeyev
Global Optimization with Non Convex Constraints Book PDF

Author : Roman G. Strongin,Yaroslav D. Sergeyev
Publisher : Springer Science & Business Media
Page : 742 pages
File Size : 41,7 Mb
Release : 2000-10-31
Category : Computers
ISBN : 0792364902

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Global Optimization with Non-Convex Constraints by Roman G. Strongin,Yaroslav D. Sergeyev Pdf

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.