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Canonical duality theory : unified methodology for multidisciplinary study

Author: David Yang Gao; Vittorio Latorre; Ning Ruan
Publisher: Cham, Switzerland : Springer, 2017.
Series: Advances in mechanics and mathematics, v. 37.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic book
Electronic books
Additional Physical Format: Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: David Yang Gao; Vittorio Latorre; Ning Ruan
ISBN: 9783319580173 3319580175 3319580167 9783319580166
OCLC Number: 1005921984
Notes: Includes index.
Description: 1 online resource : color illustrations
Contents: ""Preface""; ""Contents""; ""Canonical Duality-Triality Theory: Bridge Between Nonconvex Analysis/Mechanics and Global Optimization in Complex System""; ""1 Introduction""; ""1.1 Nonconvex Analysis/Mechanics and Difficulties""; ""1.2 Global Optimization and Challenges""; ""2 Canonical Duality-Triality Theory""; ""2.1 General Modeling and Objectivity""; ""2.2 Canonical Transformation and Classification of Nonlinearities""; ""2.3 Complementary-Dual Principle""; ""2.4 Triality Theory""; ""3 Applications for Modeling of Complex Systems""; ""3.1 Mixed Integer Nonlinear Programming"" ""3.2 Unified Model in Mathematical Physics""""4 Applications in Large Deformation Mechanics""; ""5 Applications to Computational Mechanics and Global Optimization""; ""5.1 Canonical Dual Finite Element Method""; ""5.2 Global Optimal Solutions for Discrete Nonlinear Dynamical Systems""; ""5.3 Unconstrained Nonconvex Minimization""; ""5.4 Constrained Global Optimization""; ""5.5 SDP Relaxation and Canonical Primal-Dual Algorithms""; ""6 Challenges and Breakthrough""; ""6.1 Group 1: Bi-level Duality""; ""6.2 Group 2: Conceptual Duality""; ""6.3 Group 3: Anti-triality"" ""7 Concluding Remarks and Open Problems""""References""; ""Analytic Solutions to Large Deformation Problems Governed by Generalized Neo-Hookean Model""; ""1 Nonconvex Variational Problem and Challenges""; ""2 Complete Solutions to Generalized Neo-Hookean Material""; ""3 Generalized Quasiconvexity, G-Ellipticity, and Uniqueness""; ""4 Applications in Anti-plane Shear Deformation""; ""5 Conclusions""; ""References""; ""Analytic Solutions to 3-D Finite Deformation Problems Governed by St Venant --
Kirchhoff Material""; ""1 Nonconvex Variational Problem and Motivation"" ""2 Canonical Duality Theory and Complementary Variational Principle""""3 Application to St Venant --
Kirchhoff Material""; ""3.1 Auxiliary Equation""; ""3.2 Solutions of the St. Venant --
Kirchhoff Material""; ""4 Conclusions""; ""References""; ""Remarks on Analytic Solutions and Ellipticity in Anti-plane Shear Problems of Nonlinear Elasticity""; ""1 Remarks on Nonconvex Variational Problem and Challenges""; ""2 Anti-plane Shear Deformation Problems""; ""3 Remarks on Knowles' Over-Determined Problem""; ""4 Conclusions""; ""References"" ""Canonical Duality Method for Solving Kantorovich Mass Transfer Problem""""1 Introduction""; ""2 Proof of the Main Results: Technique of Canonical Duality Method""; ""2.1 Proof of Lemma 1.1 in the Bounded Case:""; ""2.2 Proof of Theorem 1.2:""; ""2.3 Proof of Theorem 1.3:""; ""2.4 Application to Monge's Problem""; ""References""; ""Triality Theory for General Unconstrained Global Optimization Problems""; ""1 Introduction""; ""2 Canonical Duality, Triality, and Open Problem""; ""3 Strong Triality Theory""; ""4 Triality Theory for General Case""; ""5 Application""
Series Title: Advances in mechanics and mathematics, v. 37.
Responsibility: David Yang Gao, Vittorio Latorre, Ning Ruan, editors.

Abstract:

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.  Read more...

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