Multi Valued Variational Inequalities And Inclusions

Author : Siegfried Carl,Vy Khoi Le
Publisher : Springer Nature
Page : 596 pages
File Size : 53,8 Mb
Release : 2021-03-02
Category : Mathematics
ISBN : 9783030651657

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Multi-Valued Variational Inequalities and Inclusions by Siegfried Carl,Vy Khoi Le Pdf

This book focuses on a large class of multi-valued variational differential inequalities and inclusions of stationary and evolutionary types with constraints reflected by subdifferentials of convex functionals. Its main goal is to provide a systematic, unified, and relatively self-contained exposition of existence, comparison and enclosure principles, together with other qualitative properties of multi-valued variational inequalities and inclusions. The problems under consideration are studied in different function spaces such as Sobolev spaces, Orlicz-Sobolev spaces, Sobolev spaces with variable exponents, and Beppo-Levi spaces. A general and comprehensive sub-supersolution method (lattice method) is developed for both stationary and evolutionary multi-valued variational inequalities, which preserves the characteristic features of the commonly known sub-supersolution method for single-valued, quasilinear elliptic and parabolic problems. This method provides a powerful tool for studying existence and enclosure properties of solutions when the coercivity of the problems under consideration fails. It can also be used to investigate qualitative properties such as the multiplicity and location of solutions or the existence of extremal solutions. This is the first in-depth treatise on the sub-supersolution (lattice) method for multi-valued variational inequalities without any variational structures, together with related topics. The choice of the included materials and their organization in the book also makes it useful and accessible to a large audience consisting of graduate students and researchers in various areas of Mathematical Analysis and Theoretical Physics.

Author : Mikhail Z. Zgurovsky,Pavlo O. Kasyanov,Oleksiy V. Kapustyan,José Valero,Nina V. Zadoianchuk
Publisher : Springer Science & Business Media
Page : 368 pages
File Size : 46,5 Mb
Release : 2012-05-22
Category : Mathematics
ISBN : 9783642285127

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Evolution Inclusions and Variation Inequalities for Earth Data Processing III by Mikhail Z. Zgurovsky,Pavlo O. Kasyanov,Oleksiy V. Kapustyan,José Valero,Nina V. Zadoianchuk Pdf

In this sequel to two earlier volumes, the authors now focus on the long-time behavior of evolution inclusions, based on the theory of extremal solutions to differential-operator problems. This approach is used to solve problems in climate research, geophysics, aerohydrodynamics, chemical kinetics or fluid dynamics. As in the previous volumes, the authors present a toolbox of mathematical equations. The book is based on seminars and lecture courses on multi-valued and non-linear analysis and their geophysical application.

Author : Gábor Kassay,Vicențiu Rădulescu
Publisher : Academic Press
Page : 440 pages
File Size : 51,5 Mb
Release : 2018-10-09
Category : Business & Economics
ISBN : 9780128110300

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Equilibrium Problems and Applications by Gábor Kassay,Vicențiu Rădulescu Pdf

Equilibrium Problems and Applications develops a unified variational approach to deal with single-valued, set-valued and quasi-equilibrium problems. The authors promote original results in relationship with classical contributions to the field of equilibrium problems. The content evolved in the general setting of topological vector spaces and it lies at the interplay between pure and applied nonlinear analysis, mathematical economics, and mathematical physics. This abstract approach is based on tools from various fields, including set-valued analysis, variational and hemivariational inequalities, fixed point theory, and optimization. Applications include models from mathematical economics, Nash equilibrium of non-cooperative games, and Browder variational inclusions. The content is self-contained and the book is mainly addressed to researchers in mathematics, economics and mathematical physics as well as to graduate students in applied nonlinear analysis. A rigorous mathematical analysis of Nash equilibrium type problems, which play a central role to describe network traffic models, competition games or problems arising in experimental economics Develops generic models relevant to mathematical economics and quantitative modeling of game theory, aiding economists to understand vital material without having to wade through complex proofs Reveals a number of surprising interactions among various equilibria topics, enabling readers to identify a common and unified approach to analysing problem sets Illustrates the deep features shared by several types of nonlinear problems, encouraging readers to develop further this unifying approach from other viewpoints into economic models in turn

Author : James F. Peters,Yiju Yao
Publisher : Springer
Page : 810 pages
File Size : 51,8 Mb
Release : 2006-09-27
Category : Computers
ISBN : 9783540362999

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Rough Sets and Knowledge Technology by James F. Peters,Yiju Yao Pdf

This book constitutes the refereed proceedings of the First International Conference on Rough Sets and Knowledge Technology, RSKT 2006, held in Chongqing, China in July 2006. The volume presents 43 revised full papers and 58 revised short papers, together with 15 commemorative and invited papers. Topics include rough computing, evolutionary computing, fuzzy sets, granular computing, neural computing, machine learning and KDD, logics and reasoning, multiagent systems and Web intelligence, and more.

Author : Yeol Je Cho,Jong Kyu Kim
Publisher : Nova Publishers
Page : 222 pages
File Size : 41,9 Mb
Release : 2007
Category : Mathematics
ISBN : 1594548730

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Fixed Point Theory and Applications, Volume 6 by Yeol Je Cho,Jong Kyu Kim Pdf

Fixed Point Theory & Applications

Author : Anonim
Publisher : Unknown
Page : 510 pages
File Size : 53,8 Mb
Release : 2006
Category : Inequalities (Mathematics)
ISBN : UOM:39015072615340

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Advances in Nonlinear Variational Inequalities by Anonim Pdf

Author : Michael Z. Zgurovsky,Pavlo O. Kasyanov
Publisher : Springer
Page : 240 pages
File Size : 54,9 Mb
Release : 2017-07-11
Category : Technology & Engineering
ISBN : 9783319598406

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Qualitative and Quantitative Analysis of Nonlinear Systems by Michael Z. Zgurovsky,Pavlo O. Kasyanov Pdf

Here, the authors present modern methods of analysis for nonlinear systems which may occur in fields such as physics, chemistry, biology, or economics. They concentrate on the following topics, specific for such systems: (a) constructive existence results and regularity theorems for all weak solutions; (b) convergence results for solutions and their approximations; (c) uniform global behavior of solutions in time; and (d) pointwise behavior of solutions for autonomous problems with possible gaps by the phase variables. The general methodology for the investigation of dissipative dynamical systems with several applications including nonlinear parabolic equations of divergent form, nonlinear stochastic equations of parabolic type, unilateral problems, nonlinear PDEs on Riemannian manifolds with or without boundary, contact problems as well as particular examples is established. As such, the book is addressed to a wide circle of mathematical, mechanical and engineering readers.

Author : Valeri Obukhovskii,Boris Gel'man
Publisher : World Scientific
Page : 221 pages
File Size : 43,8 Mb
Release : 2020-04-04
Category : Mathematics
ISBN : 9789811220234

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Multivalued Maps And Differential Inclusions: Elements Of Theory And Applications by Valeri Obukhovskii,Boris Gel'man Pdf

The theory of multivalued maps and the theory of differential inclusions are closely connected and intensively developing branches of contemporary mathematics. They have effective and interesting applications in control theory, optimization, calculus of variations, non-smooth and convex analysis, game theory, mathematical economics and in other fields.This book presents a user-friendly and self-contained introduction to both subjects. It is aimed at 'beginners', starting with students of senior courses. The book will be useful both for readers whose interests lie in the sphere of pure mathematics, as well as for those who are involved in applicable aspects of the theory. In Chapter 0, basic definitions and fundamental results in topology are collected. Chapter 1 begins with examples showing how naturally the idea of a multivalued map arises in diverse areas of mathematics, continues with the description of a variety of properties of multivalued maps and finishes with measurable multivalued functions. Chapter 2 is devoted to the theory of fixed points of multivalued maps. The whole of Chapter 3 focuses on the study of differential inclusions and their applications in control theory. The subject of last Chapter 4 is the applications in dynamical systems, game theory, and mathematical economics.The book is completed with the bibliographic commentaries and additions containing the exposition related both to the sections described in the book and to those which left outside its framework. The extensive bibliography (including more than 400 items) leads from basic works to recent studies.

Author : J. Haslinger,M. Miettinen,Panagiotis D. Panagiotopoulos
Publisher : Springer Science & Business Media
Page : 278 pages
File Size : 46,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475752335

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Finite Element Method for Hemivariational Inequalities by J. Haslinger,M. Miettinen,Panagiotis D. Panagiotopoulos Pdf

Hemivariational inequalities represent an important class of problems in nonsmooth and nonconvex mechanics. By means of them, problems with nonmonotone, possibly multivalued, constitutive laws can be formulated, mathematically analyzed and finally numerically solved. The present book gives a rigorous analysis of finite element approximation for a class of hemivariational inequalities of elliptic and parabolic type. Finite element models are described and their convergence properties are established. Discretized models are numerically treated as nonconvex and nonsmooth optimization problems. The book includes a comprehensive description of typical representants of nonsmooth optimization methods. Basic knowledge of finite element mathematics, functional and nonsmooth analysis is needed. The book is self-contained, and all necessary results from these disciplines are summarized in the introductory chapter. Audience: Engineers and applied mathematicians at universities and working in industry. Also graduate-level students in advanced nonlinear computational mechanics, mathematics of finite elements and approximation theory. Chapter 1 includes the necessary prerequisite materials.

Author : Anonim
Publisher : Unknown
Page : 1208 pages
File Size : 50,7 Mb
Release : 2007
Category : Mathematics
ISBN : UOM:39015078588608

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Mathematical Reviews by Anonim Pdf

Author : Kyandoghere Kyamakya,Wolfgang Mathis,Ruedi Stoop,Jean Chamberlain Chedjou,Zhong Li
Publisher : Springer
Page : 367 pages
File Size : 42,9 Mb
Release : 2017-07-25
Category : Technology & Engineering
ISBN : 9783319589961

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Recent Advances in Nonlinear Dynamics and Synchronization by Kyandoghere Kyamakya,Wolfgang Mathis,Ruedi Stoop,Jean Chamberlain Chedjou,Zhong Li Pdf

This book focuses on modelling and simulation, control and optimization, signal processing, and forecasting in selected nonlinear dynamical systems, presenting both literature reviews and novel concepts. It develops analytical or numerical approaches, which are simple to use, robust, stable, flexible and universally applicable to the analysis of complex nonlinear dynamical systems. As such it addresses key challenges are addressed, e.g. efficient handling of time-varying dynamics, efficient design, faster numerical computations, robustness, stability and convergence of algorithms. The book provides a series of contributions discussing either the design or analysis of complex systems in sciences and engineering, and the concepts developed involve nonlinear dynamics, synchronization, optimization, machine learning, and forecasting. Both theoretical and practical aspects of diverse areas are investigated, specifically neurocomputing, transportation engineering, theoretical electrical engineering, signal processing, communications engineering, and computational intelligence. It is a valuable resource for students and researchers interested in nonlinear dynamics and synchronization with applications in selected areas.

Author : Nils Langenberg
Publisher : Logos Verlag Berlin GmbH
Page : 255 pages
File Size : 52,9 Mb
Release : 2011
Category : Business & Economics
ISBN : 9783832528904

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Convergence Analysis of Proximal-like Methods for Variational Inequalities and Fixed Point Problems by Nils Langenberg Pdf

Several regularization methods for variational inequalities and fixed point problems are studied. Known convergence results especially require some kind of monotonicity of the problem data as well as, especially for Bregman-function-based algorithms, some additional assumption known as the cutting plane property. Unfortunately, these assumptions may be considered as rather restrictive e.g. in the framework of Nash equilibrium problems. This motivates the development of convergence results under weaker hypotheses which constitute the major subject of the present book. Studied methods include the Bregman-function-based Proximal Point Algorithm (BPPA), Cohen's Auxiliary Problem Principle and an extragradient algorithm.Moreover, this work also contains the first numerical comparison of stopping criteria in the framework of the BPPA. Although such conditions are the subject of theoretical investigations frequently, their numerical effectiveness and a deducible preference were still unknown. This gives rise to the necessity of the presented numerical experiments.

Author : Stanisław Migórski,Anna Ochal,Mircea Sofonea
Publisher : Springer Science & Business Media
Page : 293 pages
File Size : 54,6 Mb
Release : 2012-09-18
Category : Mathematics
ISBN : 9781461442325

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Nonlinear Inclusions and Hemivariational Inequalities by Stanisław Migórski,Anna Ochal,Mircea Sofonea Pdf

This book introduces the reader the theory of nonlinear inclusions and hemivariational inequalities with emphasis on the study of contact mechanics. The work covers both abstract results in the area of nonlinear inclusions, hemivariational inequalities as well as the study of specific contact problems, including their modelling and their variational analysis. Provided results are based on original research on the existence, uniqueness, regularity and behavior of the solution for various classes of nonlinear stationary and evolutionary inclusions. In carrying out the variational analysis of various contact models, one systematically uses results of hemivariational inequalities and, in this way, illustrates the applications of nonlinear analysis in contact mechanics. New mathematical methods are introduced and applied in the study of nonlinear problems, which describe the contact between a deformable body and a foundation. Contact problems arise in industry, engineering and geophysics. Their variational analysis presented in this book lies the background for their numerical analysis. This volume will interest mathematicians, applied mathematicians, engineers, and scientists as well as advanced graduate students.

Author : Mikhail Z. Zgurovsky,Valery S. Melnik
Publisher : Springer Science & Business Media
Page : 508 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642187704

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Nonlinear Analysis and Control of Physical Processes and Fields by Mikhail Z. Zgurovsky,Valery S. Melnik Pdf

Modern achievements in the intensively developing field of applied mathematics are presented in this monograph. In particular, it proposes a new approach to extremal problem theory for nonlinear operators, differential-operator equations and inclusions, and for variational inequalities in Banach spaces. An axiomatic study of nonlinear maps (including multi-valued ones) is given, and the properties of resolving operators for systems, consisting of operator and differential-operator equations, are stated in nonlinear-map terms. The solvability conditions and the properties of extremal problem solutions are obtained, while their weak expansions and necessary conditions of optimality in variational inequality form are formulated. In addition. the monograph proposes regularization methods and approximation schemes. This book is adressed to scientists, graduates and undergraduates who are interested in nonlinear analysis, control theory, system analysis and differential equations.

Author : Igor Konnov
Publisher : Springer Science & Business Media
Page : 200 pages
File Size : 44,7 Mb
Release : 2001
Category : Business & Economics
ISBN : 3540679995

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Combined Relaxation Methods for Variational Inequalities by Igor Konnov Pdf

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.