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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.
This proceedings volume addresses advances in global optimization a
multidisciplinary research field that deals with the analysis,
characterization and computation of global minima and/or maxima of
nonlinear, non-convex and nonsmooth functions in continuous or
discrete forms. The volume contains selected papers from the third
biannual World Congress on Global Optimization in Engineering &
Science (WCGO), held in the Yellow Mountains, Anhui, China on July
8-12, 2013. The papers fall into eight topical sections:
mathematical programming; combinatorial optimization; duality
theory; topology optimization; variational inequalities and
complementarity problems; numerical optimization; stochastic models
and simulation and complex simulation and supply chain analysis."
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