Monotone
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Convex Functions Monotone Operators And Differentiability
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Author : Robert R. Phelps
language : en
Publisher: Springer
Release Date : 2013-12-11
Convex Functions Monotone Operators And Differentiability written by Robert R. Phelps and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
These notes start with an introduction to the differentiability of convex functions on Banach spaces, leading to the study of Asplund spaces and their intriguing relationship to monotone operators (and more general set-values maps) and Banach spaces with the Radon-Nikodym property. While much of this is classical, some of it is presented using streamlined proofs which were not available until recently. Considerable attention is paid to contemporary results on variational principles and perturbed optimization in Banach spaces, exhibiting their close connections with Asplund spaces. An introductory course in functional analysis is adequate background for reading these notes which can serve as the basis for a seminar of a one-term graduate course. There are numerous excercises, many of which form an integral part of the exposition.
Monotone Games
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Author : Tarun Sabarwal
language : en
Publisher: Springer Nature
Release Date : 2020-10-26
Monotone Games written by Tarun Sabarwal and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-26 with Mathematics categories.
This Palgrave Pivot examines monotone games and studies incentives and outcomes when there are multiple players, and how the decision of each player affects the well-being of others in particular ways. Games with strategic complements exhibit codirectional incentives, or incentives for each player to move in the same direction as other players. Games with strategic substitutes exhibit contradirectional incentives, or incentives for each player to move in the direction opposite to other players. Monotone games include both types of players: some players have incentives to move in the same direction as other players and some players have incentives to move in the direction opposite to other players. This book develops the theory of monotone games in a new and unified manner and presents many applications. Incentives and outcomes studied in monotone games occur in a variety of disciplines, including biology, business, computer science, economics, mathematics, medicine, philosophy, political science, and psychology, among others. The book identifies unifying threads across different cases, showing how newer results are similar to or different from previous results, and how readers may better understand them under the umbrella of monotone games.
Convex Analysis And Monotone Operator Theory In Hilbert Spaces
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Author : Heinz H. Bauschke
language : en
Publisher: Springer
Release Date : 2017-02-28
Convex Analysis And Monotone Operator Theory In Hilbert Spaces written by Heinz H. Bauschke and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-28 with Mathematics categories.
This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, machine learning, physics, decision sciences, economics, and inverse problems. The second edition of Convex Analysis and Monotone Operator Theory in Hilbert Spaces greatly expands on the first edition, containing over 140 pages of new material, over 270 new results, and more than 100 new exercises. It features a new chapter on proximity operators including two sections on proximity operators of matrix functions, in addition to several new sections distributed throughout the original chapters. Many existing results have been improved, and the list of references has been updated. Heinz H. Bauschke is a Full Professor of Mathematics at the Kelowna campus of the University of British Columbia, Canada. Patrick L. Combettes, IEEE Fellow, was on the faculty of the City University of New York and of Université Pierre et Marie Curie – Paris 6 before joining North Carolina State University as a Distinguished Professor of Mathematics in 2016.
Nonlinear Differential Equations Of Monotone Types In Banach Spaces
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Author : Viorel Barbu
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-01
Nonlinear Differential Equations Of Monotone Types In Banach Spaces written by Viorel Barbu 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 2010-01-01 with Mathematics categories.
This monograph is concerned with the basic results on Cauchy problems associated with nonlinear monotone operators in Banach spaces with applications to partial differential equations of evolutive type. It focuses on major results in recent decades.
Monotone Nonautonomous Dynamical Systems
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Author : David N. Cheban
language : en
Publisher: Springer Nature
Release Date :
Monotone Nonautonomous Dynamical Systems written by David N. Cheban and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Vector Optimization And Monotone Operators Via Convex Duality
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Author : Sorin-Mihai Grad
language : en
Publisher: Springer
Release Date : 2014-09-03
Vector Optimization And Monotone Operators Via Convex Duality written by Sorin-Mihai Grad and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-03 with Business & Economics categories.
This book investigates several duality approaches for vector optimization problems, while also comparing them. Special attention is paid to duality for linear vector optimization problems, for which a vector dual that avoids the shortcomings of the classical ones is proposed. Moreover, the book addresses different efficiency concepts for vector optimization problems. Among the problems that appear when the framework is generalized by considering set-valued functions, an increasing interest is generated by those involving monotone operators, especially now that new methods for approaching them by means of convex analysis have been developed. Following this path, the book provides several results on different properties of sums of monotone operators.
Monotone Complete C Algebras And Generic Dynamics
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Author : Kazuyuki Saitô
language : en
Publisher: Springer
Release Date : 2015-12-16
Monotone Complete C Algebras And Generic Dynamics written by Kazuyuki Saitô and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-16 with Mathematics categories.
This monograph is about monotone complete C*-algebras, their properties and the new classification theory. A self-contained introduction to generic dynamics is also included because of its important connections to these algebras. Our knowledge and understanding of monotone complete C*-algebras has been transformed in recent years. This is a very exciting stage in their development, with much discovered but with many mysteries to unravel. This book is intended to encourage graduate students and working mathematicians to attack some of these difficult questions. Each bounded, upward directed net of real numbers has a limit. Monotone complete algebras of operators have a similar property. In particular, every von Neumann algebra is monotone complete but the converse is false. Written by major contributors to this field, Monotone Complete C*-algebras and Generic Dynamics takes readers from the basics to recent advances. The prerequisites are a grounding in functional analysis, some point set topology and an elementary knowledge of C*-algebras.
Monotone Operators In Banach Space And Nonlinear Partial Differential Equations
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Author : R. E. Showalter
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-02-22
Monotone Operators In Banach Space And Nonlinear Partial Differential Equations written by R. E. Showalter and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-22 with Mathematics categories.
The objectives of this monograph are to present some topics from the theory of monotone operators and nonlinear semigroup theory which are directly applicable to the existence and uniqueness theory of initial-boundary-value problems for partial differential equations and to construct such operators as realizations of those problems in appropriate function spaces. A highlight of this presentation is the large number and variety of examples introduced to illustrate the connection between the theory of nonlinear operators and partial differential equations. These include primarily semilinear or quasilinear equations of elliptic or of parabolic type, degenerate cases with change of type, related systems and variational inequalities, and spatial boundary conditions of the usual Dirichlet, Neumann, Robin or dynamic type. The discussions of evolution equations include the usual initial-value problems as well as periodic or more general nonlocal constraints, history-value problems, those which may change type due to a possibly vanishing coefficient of the time derivative, and other implicit evolution equations or systems including hysteresis models. The scalar conservation law and semilinear wave equations are briefly mentioned, and hyperbolic systems arising from vibrations of elastic-plastic rods are developed. The origins of a representative sample of such problems are given in the appendix.
Nonlinear Ill Posed Problems Of Monotone Type
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Author : Yakov Alber
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-23
Nonlinear Ill Posed Problems Of Monotone Type written by Yakov Alber 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 2006-02-23 with Mathematics categories.
Interest in regularization methods for ill-posed nonlinear operator equations and variational inequalities of monotone type in Hilbert and Banach spaces has grown rapidly over recent years. Results in the field over the last three decades, previously only available in journal articles, are comprehensively explored with particular attention given to applications of regularization methods as well as to practical methods used in computational analysis.
Monotone Processes Of Convex And Concave Type
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Author : R. Tyrrell Rockafellar
language : en
Publisher: American Mathematical Soc.
Release Date : 1967
Monotone Processes Of Convex And Concave Type written by R. Tyrrell Rockafellar and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Convex domains categories.