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Canonical Duality Theory

Unified Methodology for Multidisciplinary Study

  • David Yang Gao
  • Vittorio Latorre
  • Ning Ruan
Book

Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 37)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Guoshan Liu, David Yang Gao, Shouyang Wang
    Pages 155-171
  3. Vittorio Latorre, Simone Sagratella, David Yang Gao
    Pages 173-185
  4. Zhong Jin, David Yang Gao
    Pages 203-221
  5. Daniel Morales-Silva, D. Y. Gao
    Pages 359-371
  6. Back Matter
    Pages 373-377

About this book

Introduction

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. 

Keywords

Canonical Duality Theory Global Optimization Solid Mechanics non-convex analysis post-buckling analysis Computational mechanics Canonical Duality-Triality Theory 3-D Finite Deformation General Unconstrained Global Optimization Problems

Editors and affiliations

  • David Yang Gao
    • 1
  • Vittorio Latorre
    • 2
  • Ning Ruan
    • 3
  1. 1.Faculty of Science and TechnologyFederation University AustraliaMt. HelenAustralia
  2. 2.Department of Computer, Control, and Managment EngineeringSapienza University of RomeRomeItaly
  3. 3.Faculty of Science and TechnologyFederation University AustraliaMt. HelenAustralia

Bibliographic information

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