Canonical Duality Theory Unified Methodology for Multidisciplinary Study [Hardcover]

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 theorys 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.

Preface.- Canonical Duality-Triality Theory: Bridge?Between Nonconvex Analysis/Mechanics and?Global Optimization in Complex System.-?Analytic Solutions to Large Deformation?Problems Governed by Generalized Neo-Hookean Model.-?Analytic Solutions to 3-D Finite Deformation?Problems Governed by St Venant-Kirchhoff?Material.-?Remarks on Analytic Solutions and Ellipticity?in Anti-Plane Shear Problems of Nonlinear?Elasticity.-?Canonical Duality Method for Solving?Kantorovich Mass Transfer Problem.-?Triality Theory for General Unconstrained?Global Optimization Problems.-?Canonical Duality Theory for Solving?Non-Monotone Variational Inl“f