Duality Principles in Nonconvex Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Duality Principles in Nonconvex Systems write by David Yang Gao. This book was released on 2013-03-09. Duality Principles in Nonconvex Systems available in PDF, EPUB and Kindle. 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.
Canonical Duality Theory
Canonical Duality Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Canonical Duality Theory write by David Yang Gao. This book was released on 2017-10-09. Canonical Duality Theory available in PDF, EPUB and Kindle. 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.
Control Of Nonlinear Distributed Parameter Systems
Control Of Nonlinear Distributed Parameter Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Control Of Nonlinear Distributed Parameter Systems write by Goong Chen. This book was released on 2001-03-14. Control Of Nonlinear Distributed Parameter Systems available in PDF, EPUB and Kindle. An examination of progress in mathematical control theory applications. It provides analyses of the influence and relationship of nonlinear partial differential equations to control systems and contains state-of-the-art reviews, including presentations from a conference co-sponsored by the National Science Foundation, the Institute of Mathematics and its Applications, the University of Minnesota, and Texas A&M University.
Duality for Nonconvex Approximation and Optimization
Duality for Nonconvex Approximation and Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Duality for Nonconvex Approximation and Optimization write by Ivan Singer. This book was released on 2007-03-12. Duality for Nonconvex Approximation and Optimization available in PDF, EPUB and Kindle. The theory of convex optimization has been constantly developing over the past 30 years. Most recently, many researchers have been studying more complicated classes of problems that still can be studied by means of convex analysis, so-called "anticonvex" and "convex-anticonvex" optimizaton problems. This manuscript contains an exhaustive presentation of the duality for these classes of problems and some of its generalization in the framework of abstract convexity. This manuscript will be of great interest for experts in this and related fields.
Advances in Applied Mathematics and Global Optimization
Advances in Applied Mathematics and Global Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Advances in Applied Mathematics and Global Optimization write by David Y. Gao. This book was released on 2009-04-09. Advances in Applied Mathematics and Global Optimization available in PDF, EPUB and Kindle. The articles that comprise this distinguished annual volume for the Advances in Mechanics and Mathematics series have been written in honor of Gilbert Strang, a world renowned mathematician and exceptional person. Written by leading experts in complementarity, duality, global optimization, and quantum computations, this collection reveals the beauty of these mathematical disciplines and investigates recent developments in global optimization, nonconvex and nonsmooth analysis, nonlinear programming, theoretical and engineering mechanics, large scale computation, quantum algorithms and computation, and information theory.
