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Full Description
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.
Contents
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 Inequality Problems.- Canonical Dual Approach for Contact Mechanics Problems with Friction.- Canonical Duality Theory for Solving Nonconvex/Discrete Constrained Global Optimization Problems.- On D.C. Optimization Problems.- Canonical Primal-Dual Method for Solving Non-convex Minimization Problems.- Unified Interior Point Methodology for Canonical Duality in Global Optimization.- Canonical Duality Theory for Topology Optimization.- Improved Canonical Dual Finite Element Method and Algorithm for Post Buckling Analysis of Nonlinear Gao Beam.- Global Solutions to Spherically Constrained Quadratic Minimization via Canonical Duality Theory.- Global Optimal Solution to QuadraticDiscrete Programming Problem with Inequality Constraints.- Global Optimal Solution to Quadratic Discrete Programming Problem with Inequality Constraints.- On Minimal Distance Between Two Surfaces.
