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Author : H. Attouch
Publisher : Pitman Advanced Publishing Program
ISBN 13 :
Total Pages : 452 pages
Book Rating : 4.:/5 (44 download)
Download or read book Variational Convergence for Functions and Operators written by H. Attouch and published by Pitman Advanced Publishing Program. This book was released on 1984 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : R. Tyrrell Rockafellar
Publisher : Springer Science & Business Media
ISBN 13 : 3642024319
Total Pages : 747 pages
Book Rating : 4.6/5 (42 download)
Download or read book Variational Analysis written by R. Tyrrell Rockafellar and published by Springer Science & Business Media. This book was released on 2009-06-26 with total page 747 pages. Available in PDF, EPUB and Kindle. Book excerpt: From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands.
Author : Omar Anza Hafsa
Publisher : World Scientific
ISBN 13 : 9811258503
Total Pages : 321 pages
Book Rating : 4.8/5 (112 download)
Download or read book Variational Convergence And Stochastic Homogenization Of Nonlinear Reaction-diffusion Problems written by Omar Anza Hafsa and published by World Scientific. This book was released on 2022-06-21 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: A substantial number of problems in physics, chemical physics, and biology, are modeled through reaction-diffusion equations to describe temperature distribution or chemical substance concentration. For problems arising from ecology, sociology, or population dynamics, they describe the density of some populations or species. In this book the state variable is a concentration, or a density according to the cases. The reaction function may be complex and include time delays terms that model various situations involving maturation periods, resource regeneration times, or incubation periods. The dynamics may occur in heterogeneous media and may depend upon a small or large parameter, as well as the reaction term. From a purely formal perspective, these parameters are indexed by n. Therefore, reaction-diffusion equations give rise to sequences of Cauchy problems.The first part of the book is devoted to the convergence of these sequences in a sense made precise in the book. The second part is dedicated to the specific case when the reaction-diffusion problems depend on a small parameter ∊ₙ intended to tend towards 0. This parameter accounts for the size of small spatial and randomly distributed heterogeneities. The convergence results obtained in the first part, with additionally some probabilistic tools, are applied to this specific situation. The limit problems are illustrated through biological invasion, food-limited or prey-predator models where the interplay between environment heterogeneities in the individual evolution of propagation species plays an essential role. They provide a description in terms of deterministic and homogeneous reaction-diffusion equations, for which numerical schemes are possible.
Author : R. Tyrrell Rockafellar
Publisher : Springer Science & Business Media
ISBN 13 : 3540627723
Total Pages : 747 pages
Book Rating : 4.5/5 (46 download)
Download or read book Variational Analysis written by R. Tyrrell Rockafellar and published by Springer Science & Business Media. This book was released on 2009-07-17 with total page 747 pages. Available in PDF, EPUB and Kindle. Book excerpt: From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands.
Author : Heinz H. Bauschke
Publisher : Springer
ISBN 13 : 3319483110
Total Pages : 624 pages
Book Rating : 4.3/5 (194 download)
Download or read book Convex Analysis and Monotone Operator Theory in Hilbert Spaces written by Heinz H. Bauschke and published by Springer. This book was released on 2017-02-28 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Franco Giannessi
Publisher : Springer Science & Business Media
ISBN 13 : 0387242767
Total Pages : 1163 pages
Book Rating : 4.3/5 (872 download)
Download or read book Variational Analysis and Applications written by Franco Giannessi and published by Springer Science & Business Media. This book was released on 2007-03-06 with total page 1163 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Volume contains the (refereed) papers presented at the 38th Conference of the School of Mathematics "G.Stampacchia" of the "E.Majorana" Centre for Scientific Culture of Erice (Sicily), held in Memory ofG. Stampacchia and J.-L. Lions in the period June 20 - July 2003. The presence of participants from Countries has greatly contributed to the success of the meeting. The School of Mathematics was dedicated to Stampacchia, not only for his great mathematical achievements, but also because He founded it. The core of the Conference has been the various features of the Variational Analysis and their motivations and applications to concrete problems. Variational Analysis encompasses a large area of modem Mathematics, such as the classical Calculus of Variations, the theories of perturbation, approximation, subgradient, subderivates, set convergence and Variational Inequalities, and all these topics have been deeply and intensely dealt during the Conference. In particular, Variational Inequalities, which have been initiated by Stampacchia, inspired by Signorini Problem and the related work of G. Fichera, have offered a very great possibility of applications to several fundamental problems of Mathematical Physics, Engineering, Statistics and Economics. The pioneer work of Stampacchia and Lions can be considered as the basic kernel around which Variational Analysis is going to be outlined and constructed. The Conference has dealt with both finite and infinite dimensional analysis, showing that to carry on these two aspects disjointly is unsuitable for both.
Author : Michael Patriksson
Publisher : Springer Science & Business Media
ISBN 13 : 147572991X
Total Pages : 343 pages
Book Rating : 4.4/5 (757 download)
Download or read book Nonlinear Programming and Variational Inequality Problems written by Michael Patriksson and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since I started working in the area of nonlinear programming and, later on, variational inequality problems, I have frequently been surprised to find that many algorithms, however scattered in numerous journals, monographs and books, and described rather differently, are closely related to each other. This book is meant to help the reader understand and relate algorithms to each other in some intuitive fashion, and represents, in this respect, a consolidation of the field. The framework of algorithms presented in this book is called Cost Approxi mation. (The preface of the Ph.D. thesis [Pat93d] explains the background to the work that lead to the thesis, and ultimately to this book.) It describes, for a given formulation of a variational inequality or nonlinear programming problem, an algorithm by means of approximating mappings and problems, a principle for the update of the iteration points, and a merit function which guides and monitors the convergence of the algorithm. One purpose of this book is to offer this framework as an intuitively appeal ing tool for describing an algorithm. One of the advantages of the framework, or any reasonable framework for that matter, is that two algorithms may be easily related and compared through its use. This framework is particular in that it covers a vast number of methods, while still being fairly detailed; the level of abstraction is in fact the same as that of the original problem statement.
Author : Van Hien Nguyen
Publisher : Springer Science & Business Media
ISBN 13 : 3642570143
Total Pages : 512 pages
Book Rating : 4.6/5 (425 download)
Download or read book Optimization written by Van Hien Nguyen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 9th Belgian-French-German Conference on Optimization has been held in Namur (Belgium) on September 7-11, 1998. This volume is a collection of papers presented at this Conference. Originally, this Conference was a French-German Conference but this year, in accordance with the organizers' wishes, a third country, Belgium, has joined the founding members of the Conference. Hence the name: Belgian French-German Conference on Optimization. Since the very beginning, the purpose of these Conferences has been to bring together researchers working in the area of Optimization and partic ularly to encourage young researchers to present their work. Most of the participants come from the organizing countries. However the general ten dancy is to invite outside researchers to attend the meeting. So this year, among the 101 participants at this Conference, twenty researchers came from other countries. The general theme of the Conference is everything that concerns the area of Optimization without specification of particular topics. So theoretical as pects of Optimization, in addition to applications and algorithms of Opti mization, will be developed. However, and this point was very important for the organizers, the Conference must retain its convivial character. No more than two parallel sessions are organized. This would allow useful contacts between researchers to be promoted. The editors express their sincere thanks to all those who took part in this Conference. Their invaluable discussions have made this volume possible.
Author : J. M. Bernardo
Publisher : Oxford University Press
ISBN 13 : 9780198526155
Total Pages : 1114 pages
Book Rating : 4.5/5 (261 download)
Download or read book Bayesian Statistics 7 written by J. M. Bernardo and published by Oxford University Press. This book was released on 2003-07-03 with total page 1114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 7th Valencia International Meeting on Bayesian Statistics. This conference is held every four years and provides the main forum for researchers in the area of Bayesian statistics to come together to present and discuss frontier developments in the field.
Author : Werner Oettli
Publisher : Springer Science & Business Media
ISBN 13 : 3642516823
Total Pages : 527 pages
Book Rating : 4.6/5 (425 download)
Download or read book Advances in Optimization written by Werner Oettli and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: This voluume contains actual contributions to the current research directions in Optimizatiton Theory as well as applications to economic problems and to problems in industrial engineering. Of particular interest are: convex- and Nonsmooth Analysis, Sensitivity Theory, Optimization techniques for nonsmooth and Variational problems, Control Theory and Vector optimization. The volume contains research andsurvey papers. The main benefit is given by a global suruvey of the state ofart of modern Optimization Theory and some typical applications.
Author : W.-M. Ni
Publisher : Springer Science & Business Media
ISBN 13 : 1461396085
Total Pages : 364 pages
Book Rating : 4.4/5 (613 download)
Download or read book Nonlinear Diffusion Equations and Their Equilibrium States II written by W.-M. Ni and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = ~U + f(u). Here ~ denotes the n-dimensional Laplacian, the solution u = u(x, t) is defined over some space-time domain of the form n x [O,T], and f(u) is a given real function whose form is determined by various physical and mathematical applications. These applications have become more varied and widespread as problem after problem has been shown to lead to an equation of this type or to its time-independent counterpart, the elliptic equation of equilibrium ~u+f(u)=O. Particular cases arise, for example, in population genetics, the physics of nu clear stability, phase transitions between liquids and gases, flows in porous media, the Lend-Emden equation of astrophysics, various simplified com bustion models, and in determining metrics which realize given scalar or Gaussian curvatures. In the latter direction, for example, the problem of finding conformal metrics with prescribed curvature leads to a ground state problem involving critical exponents. Thus not only analysts, but geome ters as well, can find common ground in the present work. The corresponding mathematical problem is to determine how the struc ture of the nonlinear function f(u) influences the behavior of the solution.
Author : Augusto Visintin
Publisher : Springer Science & Business Media
ISBN 13 : 1461240786
Total Pages : 334 pages
Book Rating : 4.4/5 (612 download)
Download or read book Models of Phase Transitions written by Augusto Visintin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: ... "What do you call work?" "Why ain't that work?" Tom resumed his whitewashing, and answered carelessly: "Well. lI1a), he it is, and maybe it aill't. All I know, is, it suits Tom Sawvc/:" "Oil CO/lll!, IIOW, Will do not mean to let 011 that you like it?" The brush continued to move. "Likc it? Well, I do not see wlzy I oughtn't to like it. Does a hoy get a chance to whitewash a fence every day?" That put the thing ill a Ilew light. Ben stopped nibhling the apple ... (From Mark Twain's Adventures of Tom Sawyer, Chapter II.) Mathematics can put quantitative phenomena in a new light; in turn applications may provide a vivid support for mathematical concepts. This volume illustrates some aspects of the mathematical treatment of phase transitions, namely, the classical Stefan problem and its generalizations. The in tended reader is a researcher in application-oriented mathematics. An effort has been made to make a part of the book accessible to beginners, as well as physicists and engineers with a mathematical background. Some room has also been devoted to illustrate analytical tools. This volume deals with research I initiated when I was affiliated with the Istituto di Analisi Numerica del C.N.R. in Pavia, and then continued at the Dipartimento di Matematica dell'Universita di Trento. It was typeset by the author in plain TEX
Author : Simeon Reich
Publisher : American Mathematical Soc.
ISBN 13 : 0821848348
Total Pages : 290 pages
Book Rating : 4.8/5 (218 download)
Download or read book Nonlinear Analysis and Optimization I written by Simeon Reich and published by American Mathematical Soc.. This book was released on 2010 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first of two volumes representing leading themes of current research in nonlinear analysis and optimization. The articles are written by prominent researchers in these two areas and bring the readers, advanced graduate students and researchers alike, to the frontline of the vigorous research in these important fields of mathematics. This volume contains articles on nonlinear analysis. Topics covered include the convex feasibility problem, fixed point theory, mathematical biology, Mosco stability, nonexpansive mapping theory, nonlinear partial differential equations, optimal control, the proximal point algorithm and semigroup theory. The companion volume (Contemporary Mathematics, Volume 514) is devoted to optimization. This book is co-published with Bar-Ilan University (Ramat-Gan, Israel). Table of Contents: A. S. Ackleh, K. Deng, and Q. Huang -- Existence-uniqueness results and difference approximations for an amphibian juvenile-adult model; S. Aizicovici, N. S. Papageorgiou, and V. Staicu -- Three nontrivial solutions for $p$-Laplacian Neumann problems with a concave nonlinearity near the origin; V. Barbu -- Optimal stabilizable feedback controller for Navier-Stokes equations; H. H. Bauschke and X. Wang -- Firmly nonexpansive and Kirszbraun-Valentine extensions: A constructive approach via monotone operator theory; R. E. Bruck -- On the random product of orthogonal projections in Hilbert space II; D. Butnariu, E. Resmerita, and S. Sabach -- A Mosco stability theorem for the generalized proximal mapping; A. Cegielski -- Generalized relaxations of nonexpansive operators and convex feasibility problems; Y. Censor and A. Segal -- Sparse string-averaging and split common fixed points; T. Dominguez Benavides and S. Phothi -- Genericity of the fixed point property for reflexive spaces under renormings; K. Goebel and B. Sims -- Mean Lipschitzian mappings; T. Ibaraki and W. Takahashi -- Generalized nonexpansive mappings and a proximal-type algorithm in Banach spaces; W. Kaczor, T. Kuczumow, and N. Michalska -- The common fixed point set of commuting nonexpansive mapping in Cartesian products of weakly compact convex sets; L. Leu'tean -- Nonexpansive iterations in uniformly convex $W$-hyperbolic spaces; G. Lopez, V. Martin-Marquez, and H.-K. Xu -- Halpern's iteration for nonexpansive mappings; J. W. Neuberger -- Lie generators for local semigroups; H.-K. Xu -- An alternative regularization method for nonexpansive mappings with applications. (CONM/513)
Author : Alexander Ioffe
Publisher : CRC Press
ISBN 13 : 100065740X
Total Pages : 278 pages
Book Rating : 4.0/5 (6 download)
Download or read book Calculus of Variations and Optimal Control written by Alexander Ioffe and published by CRC Press. This book was released on 2021-02-27 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: The calculus of variations is a classical area of mathematical analysis-300 years old-yet its myriad applications in science and technology continue to hold great interest and keep it an active area of research. These two volumes contain the referenced proceedings of the international conference on Calculus of Variations and Related Topics held at the Technion-Israel Institute of Technology in March 1998. The conference commemorated 300 years of work in the field and brought together many of its leading experts. The papers in the first volume focus on critical point theory and differential equations. The other volume deals with variational aspects of optimal control. Together they provide a unique opportunity to review the state-of-the-art of the calculus of variations, as presented by an international panel of masters in the field.
Author : Qamrul Hasan Ansari
Publisher : Springer
ISBN 13 : 8132218833
Total Pages : 362 pages
Book Rating : 4.1/5 (322 download)
Download or read book Nonlinear Analysis written by Qamrul Hasan Ansari and published by Springer. This book was released on 2014-06-05 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many of our daily-life problems can be written in the form of an optimization problem. Therefore, solution methods are needed to solve such problems. Due to the complexity of the problems, it is not always easy to find the exact solution. However, approximate solutions can be found. The theory of the best approximation is applicable in a variety of problems arising in nonlinear functional analysis and optimization. This book highlights interesting aspects of nonlinear analysis and optimization together with many applications in the areas of physical and social sciences including engineering. It is immensely helpful for young graduates and researchers who are pursuing research in this field, as it provides abundant research resources for researchers and post-doctoral fellows. This will be a valuable addition to the library of anyone who works in the field of applied mathematics, economics and engineering.
Author : Shouchuan Hu
Publisher : Springer Nature
ISBN 13 : 3031178378
Total Pages : 544 pages
Book Rating : 4.0/5 (311 download)
Download or read book Research Topics in Analysis, Volume I written by Shouchuan Hu and published by Springer Nature. This book was released on 2022-11-29 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, which is the first of two volumes, presents, in a unique way, some of the most relevant research tools of modern analysis. This work empowers young researchers with all the necessary techniques to explore the various subfields of this broad subject, and introduces relevant frameworks where these tools can be immediately deployed. Volume I starts with the foundations of modern analysis. The first three chapters are devoted to topology, measure theory, and functional analysis. Chapter 4 offers a comprehensive analysis of the main function spaces, while Chapter 5 covers more concrete subjects, like multivariate analysis, which are closely related to applications and more difficult to find in compact form. Chapter 6 deals with smooth and non-smooth calculus of functions; Chapter 7 introduces certain important classes of nonlinear operators; and Chapter 8 complements the previous three chapters with topics of variational analysis. Each chapter of this volume finishes with a list of problems – handy for understanding and self-study – and historical notes that give the reader a more vivid picture of how the theory developed. Volume II consists of various applications using the tools and techniques developed in this volume. By offering a clear and wide picture of the tools and applications of modern analysis, this work can be of great benefit not only to mature graduate students seeking topics for research, but also to experienced researchers with an interest in this vast and rich field of mathematics.
Author : Kok Keong Tan
Publisher : World Scientific
ISBN 13 : 9814554308
Total Pages : 394 pages
Book Rating : 4.8/5 (145 download)
Download or read book Fixed Point Theory And Applications - Proceedings Of The Second International Conference written by Kok Keong Tan and published by World Scientific. This book was released on 1992-08-08 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains current works of researchers from twelve different countries on fixed point theory and applications. Topics include, in part, nonexpansive mappings, multifunctions, minimax inequalities, applications to game theory and computation of fixed points. It is valuable to pure and applied mathematicians as well as computing scientists and mathematical economists.
