Combined Relaxation Methods For Variational Inequalities

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Combined Relaxation Methods For Variational Inequalities

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Author : Igor Konnov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Combined Relaxation Methods For Variational Inequalities written by Igor Konnov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.

Variational inequalities proved to be a very useful and powerful tool for in vestigation and solution of many equilibrium type problems in Economics, Engineering, Operations Research and Mathematical Physics. In fact, varia tional inequalities for example provide a unifying framework for the study of such diverse problems as boundary value problems, price equilibrium prob lems and traffic network equilibrium problems. Besides, they are closely re lated with many general problems of Nonlinear Analysis, such as fixed point, optimization and complementarity problems. As a result, the theory and so lution methods for variational inequalities have been studied extensively, and considerable advances have been made in these areas. This book is devoted to a new general approach to constructing solution methods for variational inequalities, which was called the combined relax ation (CR) approach. This approach is based on combining, modifying and generalizing ideas contained in various relaxation methods. In fact, each com bined relaxation method has a two-level structure, i.e., a descent direction and a stepsize at each iteration are computed by finite relaxation procedures.

Combined Relaxation Methods For Variational Inequalities

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Author : Igor Konnov
language : en
Publisher: Springer
Release Date : 2011-04-27

Combined Relaxation Methods For Variational Inequalities written by Igor Konnov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-27 with categories.

Variational inequalities proved to be a very useful tool for investigation and solution of various equilibrium type problems arising in Economics, Operations Research, Mathematical Physics, and Transportation. This book is devoted to a new general approach to constructing solution methods for variational inequalities, which was called the combined relaxation approach. This approach is rather flexible and allows one to construct various methods both for single-valued and for multi-valued variational inequalities, including nonlinear constrained problems. The other essential feature of the combined relaxation methods is that they are convergent under very mild assumptions. The book can be viewed as an attempt to discribe the existing combined relaxation methods as a whole.

Integrability Of Nonlinear Systems

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Author : Yvette Kosmann-Schwarzbach
language : en
Publisher: Springer
Release Date : 1997-11-18

Integrability Of Nonlinear Systems written by Yvette Kosmann-Schwarzbach and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-11-18 with Science categories.

The theory of nonlinear systems and, in particular, of integrable systems is related to several very active fields of research in theoretical physics. Many mathematical aspects of nonlinear systems, both continuous and discrete, are analyzed here with particular emphasis on the domains of inverse-scattering techniques, singularity analysis, the bilinear formalism, chaos in nonlinear oscillators, Lie-algebraic and group-theoretical methods, classical and quantum integrability, bihamiltonian structures. The book will be of considerable interest to those who wish to study integrable systems, and to follow the future developments, both in mathematics and in theoretical physics, of the theory of integrability.

Network Economics

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Author : Anna Nagurney
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-12-31

Network Economics written by Anna Nagurney and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-12-31 with Business & Economics categories.

The second and revised edition of Network Economics: A Variational Inequality Approach provides an updated treatment of network economics through the inclusion of new theoretical results and new applications, as well as problems for self-study purposes and/or for use in the classroom. This volume remains true to the first edition in that it provides a unified treatment of finite-dimensional variational inequalities, algorithms, and applications. Physical networks are pervasive in today's society in the form of transportation networks, telecommunication networks, energy networks, and financial networks, whereas mathematical networks provide a mechanism for studying a plethora of economic equilibrium problems through a common graphic structure. Network Economics establishes the connections among economic equilibrium problems through their network structure and demonstrates how the structure can then be used to address policy interventions, as well as to construct efficient numerical schemes for the computation of equilibria. The network framework provides not only a mechanism for the graphic representation of economic problems and a means for visualizing their similarities and differences, but, in addition, a novel theoretical approach. Problems treated include: congested transportation systems, oligopolistic market equilibrium problems, problems of human migration, and general financial and economic equilibrium problems. New applications covered in this second edition include environmental networks and knowledge networks.

Uncertainty Quantification In Variational Inequalities

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Author : Joachim Gwinner
language : en
Publisher: CRC Press
Release Date : 2021-12-21

Uncertainty Quantification In Variational Inequalities written by Joachim Gwinner and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-21 with Mathematics categories.

Uncertainty Quantification (UQ) is an emerging and extremely active research discipline which aims to quantitatively treat any uncertainty in applied models. The primary objective of Uncertainty Quantification in Variational Inequalities: Theory, Numerics, and Applications is to present a comprehensive treatment of UQ in variational inequalities and some of its generalizations emerging from various network, economic, and engineering models. Some of the developed techniques also apply to machine learning, neural networks, and related fields. Features First book on UQ in variational inequalities emerging from various network, economic, and engineering models Completely self-contained and lucid in style Aimed for a diverse audience including applied mathematicians, engineers, economists, and professionals from academia Includes the most recent developments on the subject which so far have only been available in the research literature

Generalized Convexity And Related Topics

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Author : Igor V. Konnov
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-22

Generalized Convexity And Related Topics written by Igor V. Konnov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-22 with Business & Economics categories.

The book contains invited papers by well-known experts on a wide range of topics (economics, variational analysis, probability etc.) closely related to convexity and generalized convexity, and refereed contributions of specialists from the world on current research on generalized convexity and applications, in particular, to optimization, economics and operations research.

Finite Dimensional Variational Inequalities And Complementarity Problems

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Author : Francisco Facchinei
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-04

Finite Dimensional Variational Inequalities And Complementarity Problems written by Francisco Facchinei and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-04 with Business & Economics categories.

The ?nite-dimensional nonlinear complementarity problem (NCP) is a s- tem of ?nitely many nonlinear inequalities in ?nitely many nonnegative variables along with a special equation that expresses the complementary relationship between the variables and corresponding inequalities. This complementarity condition is the key feature distinguishing the NCP from a general inequality system, lies at the heart of all constrained optimi- tion problems in ?nite dimensions, provides a powerful framework for the modeling of equilibria of many kinds, and exhibits a natural link between smooth and nonsmooth mathematics. The ?nite-dimensional variational inequality (VI), which is a generalization of the NCP, provides a broad unifying setting for the study of optimization and equilibrium problems and serves as the main computational framework for the practical solution of a host of continuum problems in the mathematical sciences. The systematic study of the ?nite-dimensional NCP and VI began in the mid-1960s; in a span of four decades, the subject has developed into a very fruitful discipline in the ?eld of mathematical programming. The - velopments include a rich mathematical theory, a host of e?ective solution algorithms, a multitude of interesting connections to numerous disciplines, and a wide range of important applications in engineering and economics. As a result of their broad associations, the literature of the VI/CP has bene?ted from contributions made by mathematicians (pure, applied, and computational), computer scientists, engineers of many kinds (civil, ch- ical, electrical, mechanical, and systems), and economists of diverse exp- tise (agricultural, computational, energy, ?nancial, and spatial).

Vector Variational Inequalities And Vector Optimization

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Author : Qamrul Hasan Ansari
language : en
Publisher: Springer
Release Date : 2017-10-31

Vector Variational Inequalities And Vector Optimization written by Qamrul Hasan Ansari and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-31 with Business & Economics categories.

This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems. It is the first-ever book to introduce well-posedness and sensitivity analysis for vector equilibrium problems. The first chapter provides basic notations and results from the areas of convex analysis, functional analysis, set-valued analysis and fixed-point theory for set-valued maps, as well as a brief introduction to variational inequalities and equilibrium problems. Chapter 2 presents an overview of analysis over cones, including continuity and convexity of vector-valued functions. The book then shifts its focus to solution concepts and classical methods in vector optimization. It describes the formulation of vector variational inequalities and their applications to vector optimization, followed by separate chapters on linear scalarization, nonsmooth and generalized vector variational inequalities. Lastly, the book introduces readers to vector equilibrium problems and generalized vector equilibrium problems. Written in an illustrative and reader-friendly way, the book offers a valuable resource for all researchers whose work involves optimization and vector optimization.

Advances In Variational And Hemivariational Inequalities

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Author : Weimin Han
language : en
Publisher: Springer
Release Date : 2015-03-02

Advances In Variational And Hemivariational Inequalities written by Weimin Han and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-02 with Mathematics categories.

This volume is comprised of articles providing new results on variational and hemivariational inequalities with applications to Contact Mechanics unavailable from other sources. The book will be of particular interest to graduate students and young researchers in applied and pure mathematics, civil, aeronautical and mechanical engineering, and can be used as supplementary reading material for advanced specialized courses in mathematical modeling. New results on well posedness to stationary and evolutionary inequalities and their rigorous proofs are of particular interest to readers. In addition to results on modeling and abstract problems, the book contains new results on the numerical methods for variational and hemivariational inequalities.

Handbook Of Generalized Convexity And Generalized Monotonicity

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Author : Nicolas Hadjisavvas
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-16

Handbook Of Generalized Convexity And Generalized Monotonicity written by Nicolas Hadjisavvas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-16 with Mathematics categories.

Studies in generalized convexity and generalized monotonicity have significantly increased during the last two decades. Researchers with very diverse backgrounds such as mathematical programming, optimization theory, convex analysis, nonlinear analysis, nonsmooth analysis, linear algebra, probability theory, variational inequalities, game theory, economic theory, engineering, management science, equilibrium analysis, for example are attracted to this fast growing field of study. Such enormous research activity is partially due to the discovery of a rich, elegant and deep theory which provides a basis for interesting existing and potential applications in different disciplines. The handbook offers an advanced and broad overview of the current state of the field. It contains fourteen chapters written by the leading experts on the respective subject; eight on generalized convexity and the remaining six on generalized monotonicity.