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.
Duality Principles in Nonconvex Systems
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.
Conjugate Duality and Optimization
Conjugate Duality 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 Conjugate Duality and Optimization write by R. Tyrrell Rockafellar. This book was released on 1974-01-01. Conjugate Duality and Optimization available in PDF, EPUB and Kindle. Provides a relatively brief introduction to conjugate duality in both finite- and infinite-dimensional problems. An emphasis is placed on the fundamental importance of the concepts of Lagrangian function, saddle-point, and saddle-value. General examples are drawn from nonlinear programming, approximation, stochastic programming, the calculus of variations, and optimal control.
Duality in Optimization and Variational Inequalities
Duality in Optimization and Variational Inequalities - 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 in Optimization and Variational Inequalities write by C.j. Goh. This book was released on 2002-05-10. Duality in Optimization and Variational Inequalities available in PDF, EPUB and Kindle. This comprehensive volume covers a wide range of duality topics ranging from simple ideas in network flows to complex issues in non-convex optimization and multicriteria problems. In addition, it examines duality in the context of variational inequalities and vector variational inequalities, as generalizations to optimization. Duality in Optimization and Variational Inequalities is intended for researchers and practitioners of optimization with the aim of enhancing their understanding of duality. It provides a wider appreciation of optimality conditions in various scenarios and under different assumptions. It will enable the reader to use duality to devise more effective computational methods, and to aid more meaningful interpretation of optimization and variational inequality problems.
Duality and Approximation Methods for Cooperative Optimization and Control
Duality and Approximation Methods for Cooperative Optimization and Control - 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 and Approximation Methods for Cooperative Optimization and Control write by Mathias Bürger. This book was released on 2014. Duality and Approximation Methods for Cooperative Optimization and Control available in PDF, EPUB and Kindle. This thesis investigates the role of duality and the use of approximation methods in cooperative optimization and control. Concerning cooperative optimization, a general algorithm for convex optimization in networks with asynchronous communication is presented. Based on the idea of polyhedral approximations, a family of distributed algorithms is developed to solve a variety of distributed decision problems, ranging from semi-definite and robust optimization problems up to distributed model predictive control. Optimization theory, and in particular duality theory, are shown to be central elements also in cooperative control. This thesis establishes an intimate relation between passivity-based cooperative control and network optimization theory. The presented results provide a complete duality theory for passivity-based cooperative control and lead the way to novel analysis tools for complex dynamic phenomena. In this way, this thesis presents theoretical insights and algorithmic approaches for cooperative optimization and control, and emphasizes the role of convexity and duality in this field.
