Convex Analysis and Monotone Operator Theory in Hilbert Spaces

Author: Heinz H. Bauschke,Patrick L. Combettes

Publisher: Springer

ISBN: 3319483110

Category: Mathematics

Page: 619

View: 850

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.
Posted in Mathematics

Convex analysis and optimization in Hadamard spaces

Author: Miroslav Bacak

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110361620

Category: Mathematics

Page: 193

View: 6831

This book gives a first systematic account on the subject of convex analysis and optimization in Hadamard spaces. It is primarily aimed at both graduate students and researchers in analysis and optimization.
Posted in Mathematics


From Concepts to Applications

Author: Jean-Paul Penot

Publisher: Springer

ISBN: 331932411X

Category: Mathematics

Page: 669

View: 9979

This textbook covers the main results and methods of real analysis in a single volume. Taking a progressive approach to equations and transformations, this book starts with the very foundations of real analysis (set theory, order, convergence, and measure theory) before presenting powerful results that can be applied to concrete problems. In addition to classical results of functional analysis, differential calculus and integration, Analysis discusses topics such as convex analysis, dissipative operators and semigroups which are often absent from classical treatises. Acknowledging that analysis has significantly contributed to the understanding and development of the present world, the book further elaborates on techniques which pervade modern civilization, including wavelets in information theory, the Radon transform in medical imaging and partial differential equations in various mechanical and physical phenomena. Advanced undergraduate and graduate students, engineers as well as practitioners wishing to familiarise themselves with concepts and applications of analysis will find this book useful. With its content split into several topics of interest, the book’s style and layout make it suitable for use in several courses, while its self-contained character makes it appropriate for self-study.
Posted in Mathematics

New Trends in Differential Equations, Control Theory and Optimization

Proceedings of the 8th Congress of Romanian Mathematicians

Author: Viorel Barbu,Cătălin Lefter,Ioan I Vrabie

Publisher: World Scientific

ISBN: 9813142871

Category: Mathematics

Page: 348

View: 9345

The volume contains a collection of original papers and surveys in various areas of Differential Equations, Control Theory and Optimization written by well-known specialists and is thus useful for PhD students and researchers in applied mathematics. Contents:Dirichlet Problems with Mean Curvature Operator in Minkowski Space (Cristian Bereanu, Petru Jebelean and Călin Şerban)Free Boundary Fluid-Elasticity Interactions: Adjoint Sensitivity Analysis (Lorena Bociu and Kristina Martin)Non-Smooth Regularization of a Forward-Backward Parabolic Equation (Elena Bonetti, Pierluigi Colli and Giuseppe Tomassetti)Approaching Monotone Inclusion Problems via Second Order Dynamical Systems with Linear and Anisotropic Damping (Radu Ioan Boţ and Ernö Robert Csetnek)On the Solutions of a Quadratic Integral Inclusion (Aurelian Cernea)On the Bounded and Stabilizing Solution of a Generalized Riccati Differential Equation with Periodic Coefficients Arising in Connection with a Zero Sum Linear Quadratic Stochastic Differential Game (Vasile Dragan and Toader Morozan)A Maximum Principle for a Class of First Order Differential Operators (Maria Fărcăşeanu, Mihai Mihăilescu and Denisa Stancu-Dumitru)Differentiability and Integrability Properties for Solutions to Nonlocal Equations (Mikil Foss and Petronela Radu)Ferroelectric Thin Structures (Antonio Gaudiello and Kamel Hamdache)Sliding Modes for a Phase-Field System (Gianni Gilardi)Uniformly Hyperbolic Viable Sets in Affine IFS (Vasile Glavan and Valeriu Guţu)Some Support Considerations in the Asymptotic Optimality of Two-Scale Controlled PDMP (Dan Goreac and Oana Silvia Serea)Inverse Problems for Control Theory (Mohammed Al Horani and Angelo Favini)On the Ill-Posedness of Active Scalar Equations with Odd Singular Kernels (Igor Kukavica, Vlad Vicol and Fei Wang)Equilibrium in an Individual — Societal SIR Vaccination Model in Presence of Discounting and Finite Vaccination Capacity (Laetitia Laguzet, Gabriel Turinici and Ghozlane Yahiaoui)On Some Minimization Problems in RN (Mihai Mariş)Recent Results on Multiple Periodic Solutions of Forced Relativistic Pendulum-Type Continuous and Discrete Systems (Jean Mawhin)On the Anisotropic Caginalp Phase-Field System with Singular Nonlinear Terms (Alain Miranville)Space, Time, Similarity (Umberto Mosco)Singularly Perturbed Problems for Abstract Differential Equations of Second Order in Hilbert Spaces (Andrei Perjan and Galina Rusu)Global Controllability and Mixing for the Burgers Equation with Localised Finite-Dimensional External Force (Armen Shirikyan)Boundary Observation in Shape Optimization (Dan Tiba)Recent Progress on Steady Gravity Water Waves (Eugen Vărvărucă) Readership: Researchers in partial differential equations, calculus of variations and optimal control, difference and functional equations.
Posted in Mathematics

Algorithmen und Datenstrukturen


Author: Niklaus Wirth

Publisher: Springer-Verlag

ISBN: 3322947041

Category: Technology & Engineering

Page: 320

View: 7013

In den vergangenen Jahren wurde die Programmierung wm Rechenanlagen als diejenige Disziplin erkannt, deren Beherrschung grundlegend und entscheidend für den Erfolg vieler Entwicklungsprojekte ist und die wissenschaftlicher Behandlung und Darlegung zugänglich ist Vom Handwerk stieg sie zur akademischen Disziplin auf. Die ersten hervorragenden Beiträge zu dieser Entwicklung wurden von E. W. Dijkstra und C. A. R. Hoare geliefert Dijkstra's Notes on Struetured Programming [6J führten zu einer neuen Betrachtung der Programmierung als wissenschaftliches Thema und als intellektuelle Herausforderung. Sie bahnten den Weg zu einer "Revolution" in der Programmierung [35J. Hoare's An Axiommic Ba3is for Computer Programming [10J zeigte deutlich, dass Progamme einer exakten Analyse nach mathematischen Grundsätzen zugänglich sind. Beide Artikel argumentieren überzeugend, dass viele Programmierfehler vermieden werden können, wenn man den Programmierern die Methoden und Techniken, die sie bisher intuitiv und oft unbewusst verwendeten, zur Kenntnis bringt Diese Artikel konzentrierten sich auf die Aspekte des Aufbauens und Analysierens von Programmen oder, genauer ausgedruckt, auf die Struktur der durch die Progammtexte dargestellten Algorithmen. Es ist jedoch völlig klar, dass ein systematisches und wissenschaftliches Angehen der Konstruktion von Programmen seine grösste Wirkung im Fall grosser komplexer Programme hat, die komplizierte Datenmengen bearbeiten. Folglich muss eine Methodik des Programmierens auch alle Aspekte der Datenstrukturierung behandeln. Programme sind letztlich konkrete Formulierungen abstrakter Algorithmen, die sich auf bestimmte Darstellungen und Datenstrukturen stützen. Einen wesentlichen Beitrag, Ordnung in die verwirrende Vielfalt der Terminologie und Konzepte von Datenstrukturen zu bringen, leistete Hoare durch seine Notes on Daltl Strueturing [13J.
Posted in Technology & Engineering

Vorlesungen über einige Klassen Nichtlinearer Integralgleichungen und Integro-Differentialgleichungen

Nebst Anwendungen

Author: Leon Lichtenstein

Publisher: Springer-Verlag

ISBN: 3642476007

Category: Mathematics

Page: 166

View: 8864

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
Posted in Mathematics

Lehrbuch der Analysis

Author: Rudolf Lipschitz

Publisher: N.A


Category: Calculus

Page: 734

View: 7888

Posted in Calculus

Theorie der konvexen Körper

Author: T. Bonnesen,W. Fenchel

Publisher: Springer-Verlag

ISBN: 364293014X

Category: Mathematics

Page: 168

View: 9252

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
Posted in Mathematics

Computational and Analytical Mathematics

In Honor of Jonathan Borwein's 60th Birthday

Author: David H. Bailey,Heinz H. Bauschke,Peter Borwein,Frank Garvan,Michel Théra,Jon D. Vanderwerff,Henry Wolkowicz

Publisher: Springer Science & Business Media

ISBN: 1461476216

Category: Mathematics

Page: 701

View: 2759

The research of Jonathan Borwein has had a profound impact on optimization, functional analysis, operations research, mathematical programming, number theory, and experimental mathematics. Having authored more than a dozen books and more than 300 publications, Jonathan Borwein is one of the most productive Canadian mathematicians ever. His research spans pure, applied, and computational mathematics as well as high performance computing, and continues to have an enormous impact: MathSciNet lists more than 2500 citations by more than 1250 authors, and Borwein is one of the 250 most cited mathematicians of the period 1980-1999. He has served the Canadian Mathematics Community through his presidency (2000–02) as well as his 15 years of editing the CMS book series. Jonathan Borwein’s vision and initiative have been crucial in initiating and developing several institutions that provide support for researchers with a wide range of scientific interests. A few notable examples include the Centre for Experimental and Constructive Mathematics and the IRMACS Centre at Simon Fraser University, the Dalhousie Distributed Research Institute at Dalhousie University, the Western Canada Research Grid, and the Centre for Computer Assisted Research Mathematics and its Applications, University of Newcastle. The workshops that were held over the years in Dr. Borwein’s honor attracted high-caliber scientists from a wide range of mathematical fields. This present volume is an outgrowth of the workshop on ‘Computational and Analytical Mathematics’ held in May 2011 in celebration of Dr. Borwein’s 60th Birthday. The collection contains various state-of-the-art research manuscripts and surveys presenting contributions that have risen from the conference, and is an excellent opportunity to survey state-of-the-art research and discuss promising research directions and approaches.
Posted in Mathematics

Kreis und Kugel

Author: Wilhelm Blaschke

Publisher: Walter de Gruyter

ISBN: 3111506932

Category: Mathematics

Page: 175

View: 5615

Posted in Mathematics

Analysis II

Author: Vladimir A. Zorich

Publisher: Springer

ISBN: 9783540462316

Category: Mathematics

Page: 708

View: 9815

Ausführlich, klar, exakt, solide: die Anfänge der Analysis in 2 Bänden. Von der Einführung der reellen Zahlen bis hin zu fortgeschrittenen Themen wie u.a. Differenzialformen auf Mannigfaltigkeiten, asymptotische Betrachtungen, Fourier-, Laplace- und Legendre-Transformationen, elliptische Funktionen und Distributionen. Deutlich auf naturwissenschaftliche Fragen ausgerichtet, erläutert dieses Werk detailliert Begriffe, Inhalte und Sätze der Integral- und Differenzialrechnung. Die Fülle hilfreicher Beispiele, Aufgaben und Anwendungen ist selten in Analysisbüchern zu finden. Band 2 beschreibt den heutigen Stand der klassischen Analysis.
Posted in Mathematics

Regular Solids and Isolated Singularities

Author: Klaus Lamotke

Publisher: Vieweg+Teubner Verlag

ISBN: 9783528089580

Category: Mathematics

Page: 224

View: 9599

The last book XIII of Euclid's Elements deals with the regular solids which therefore are sometimes considered as crown of classical geometry. More than two thousand years later around 1850 Schl~fli extended the classification of regular solids to four and more dimensions. A few decades later, thanks to the invention of group and invariant theory the old three dimensional regular solid were involved in the development of new mathematical ideas: F. Klein (Lectures on the Icosa hedron and the Resolution of Equations of Degree Five, 1884) emphasized the relation of the regular solids to the finite rotation groups. He introduced complex coordinates and by means of invariant theory associated polynomial equations with these groups. These equations in turn describe isolated singularities of complex surfaces. The structure of the singularities is investigated by methods of commutative algebra, algebraic and complex analytic geometry, differential and algebraic topology. A paper by DuVal from 1934 (see the References), in which resolutions play an important rele, marked an early stage of these investigations. Around 1970 Klein's polynomials were again related to new mathematical ideas: V. I. Arnold established a hierarchy of critical points of functions in several variables according to growing com plexity. In this hierarchy Kleinls polynomials describe the "simple" critical points.
Posted in Mathematics

Mathematical Reviews

Author: N.A

Publisher: N.A


Category: Mathematics

Page: N.A

View: 5790

Posted in Mathematics

Convex Functions and Their Applications

A Contemporary Approach

Author: Constantin P. Niculescu,Lars-Erik Persson

Publisher: Springer

ISBN: 3319783378

Category: Mathematics

Page: 415

View: 4614

Thorough introduction to an important area of mathematics Contains recent results Includes many exercises
Posted in Mathematics

Meine Zahlen, meine Freunde

Glanzlichter der Zahlentheorie

Author: Paulo Ribenboim

Publisher: Springer-Verlag

ISBN: 3540879579

Category: Mathematics

Page: 391

View: 1259

Paulo Ribenboim behandelt Zahlen in dieser außergewöhnlichen Sammlung von Übersichtsartikeln wie seine persönlichen Freunde. In leichter und allgemein zugänglicher Sprache berichtet er über Primzahlen, Fibonacci-Zahlen (und das Nordpolarmeer!), die klassischen Arbeiten von Gauß über binäre quadratische Formen, Eulers berühmtes primzahlerzeugendes Polynom, irrationale und transzendente Zahlen. Nach dem großen Erfolg von „Die Welt der Primzahlen" ist dies das zweite Buch von Paulo Ribenboim, das in deutscher Sprache erscheint.
Posted in Mathematics

Analysis und mathematische Physik

Author: Hans Triebel

Publisher: Springer-Verlag

ISBN: 3034852657

Category: Juvenile Nonfiction

Page: 451

View: 5655

Posted in Juvenile Nonfiction

Real and Abstract Analysis

A modern treatment of the theory of functions of a real variable

Author: Edwin Hewitt,Karl Stromberg

Publisher: Springer-Verlag

ISBN: 3662297949

Category: Mathematics

Page: 476

View: 5961

Posted in Mathematics

Constructive, Experimental, and Nonlinear Analysis

Author: Michel A. Théra

Publisher: American Mathematical Soc.

ISBN: 9780821821671

Category: Mathematics

Page: 289

View: 3985

This volume presents twenty original refereed papers on different aspects of modern analysis, including analytic and computational number theory, symbolic and numerical computation, theoretical and computational optimization, and recent development in nonsmooth and functional analysis with applications to control theory. These papers originated largely from a conference held in conjunction with a 1999 Doctorate Honoris Causa awarded to Jonathan Borwein at Limoges. As such they reflect the areas in which Dr. Borwein has worked. In addition to providing a snapshot of research in the field of modern analysis, the papers suggest some of the directions this research is following at the beginning of the millennium.
Posted in Mathematics

Analysis I

Author: Herbert Amann,Joachim Escher

Publisher: Springer-Verlag

ISBN: 3034877943

Category: Mathematics

Page: 445

View: 5188

Dieses Lehrbuch ist der erste Band einer dreiteiligen Einführung in die Analysis. Es ist durch einen modernen und klaren Aufbau geprägt, der versucht den Blick auf das Wesentliche zu richten. Anders als in den üblichen Lehrbüchern wird keine künstliche Trennung zwischen der Theorie einer Variablen und derjenigen mehrerer Veränderlicher vorgenommen. Der Leser soll in dem Erkennen der wesentlichen Inhalte und Ideen der Analysis geschult werden und sich ein solides Fundament für das Studium tieferliegender Theorien erwerben. Das Werk richtet sich an Hörer und Dozenten der Anfängervorlesung der Analysis. Durch zahlreiche Beispiele, Übungsaufgaben und Ergänzungen zum üblichen Vorlesungsstoff ist der Text ausserdem zum Selbststudium, als Vorlage für vertiefende Seminare und als Grundlage für das gesamte Mathematik- bzw. Physikstudium geeignet.
Posted in Mathematics