Canonical duality theory : unified methodology for multidisciplinary study /: unified methodology for multidisciplinary study. (2017)

• Record Type: Book
• Further Information: Note: David Yang Gao, Vittorio Latorre, Ning Ruan, editors.
• Editors: Gao, David Yang; Latorre, Vittorio; Ruan, Ning
• 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""
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2017
• Extent: 1 online resource, color illustrations
• Subjects: 515/.782; Mathematics; Duality theory (Mathematics); MATHEMATICS -- Calculus; MATHEMATICS -- Mathematical Analysis; Duality theory (Mathematics); Science -- Mechanics -- General; Classical mechanics; Mathematical optimization; Mechanics; Mathematics -- Applied; Optimization; Electronic books
• Languages: English
• ISBNs: 9783319580173; 3319580175; 3319580167; 9783319580166
• Related ISBNs: 9783319580166
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed October 23, 2017).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.