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Duality Principles in Nonconvex Systems - Theory, Methods and Applications (Paperback, Softcover reprint of hardcover 1st ed. 2000)
Loot Price: R3,742
Discovery Miles 37 420
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Duality Principles in Nonconvex Systems - Theory, Methods and Applications (Paperback, Softcover reprint of hardcover 1st ed. 2000)
Series: Nonconvex Optimization and Its Applications, 39
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Motivated by practical problems in engineering and physics, drawing
on a wide range of applied mathematical disciplines, this book is
the first to provide, within a unified framework, a self-contained
comprehensive mathematical theory of duality for general
non-convex, non-smooth systems, with emphasis on methods and
applications in engineering mechanics. Topics covered include the
classical (minimax) mono-duality of convex static equilibria, the
beautiful bi-duality in dynamical systems, the interesting
tri-duality in non-convex problems and the complicated
multi-duality in general canonical systems. A potentially powerful
sequential canonical dual transformation method for solving fully
nonlinear problems is developed heuristically and illustrated by
use of many interesting examples as well as extensive applications
in a wide variety of nonlinear systems, including differential
equations, variational problems and inequalities, constrained
global optimization, multi-well phase transitions, non-smooth
post-bifurcation, large deformation mechanics, structural limit
analysis, differential geometry and non-convex dynamical systems.
With exceptionally coherent and lucid exposition, the work fills a
big gap between the mathematical and engineering sciences. It shows
how to use formal language and duality methods to model natural
phenomena, to construct intrinsic frameworks in different fields
and to provide ideas, concepts and powerful methods for solving
non-convex, non-smooth problems arising naturally in engineering
and science. Much of the book contains material that is new, both
in its manner of presentation and in its research development. A
self-contained appendix provides some necessary background from
elementary functional analysis. Audience: The book will be a
valuable resource for students and researchers in applied
mathematics, physics, mechanics and engineering. The whole volume
or selected chapters can also be recommended as a text for both
senior undergraduate and graduate courses in applied mathematics,
mechanics, general engineering science and other areas in which the
notions of optimization and variational methods are employed.
General
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