# Canonical Duality Theory

## Unified Methodology for Multidisciplinary Study

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

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

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.

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

- DOI https://doi.org/10.1007/978-3-319-58017-3
- Copyright Information Springer International Publishing AG 2017
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-319-58016-6
- Online ISBN 978-3-319-58017-3
- Series Print ISSN 1571-8689
- Series Online ISSN 1876-9896
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