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Approximation theory. --- Monotone operators. --- Théorie de l'approximation --- Opérateurs monotones
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Operator theory --- Approximation theory. --- Spaces of measures. --- Espaces de mesures. --- Numerical analysis. --- Opérateurs monotones --- Ensembles ordonnés --- Ordered sets --- Monotone operators --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Mathematical analysis --- Espaces vectoriels topologiques ordonnés --- Linear topological spaces, Ordered --- Fonctions continues --- Functions, Continuous --- Opérateurs monotones --- Ensembles ordonnés --- Espaces vectoriels topologiques ordonnés. --- Opérateurs monotones. --- Ensembles ordonnés. --- Approximation, Théorie de l' --- Approximation, Théorie de l' --- Ensembles ordonnés. --- Espaces vectoriels topologiques ordonnés. --- Opérateurs monotones.
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Convex functions --- Differentiable functions --- Monotone operators --- Fonctions convexes --- Fonctions différentiables --- Opérateurs monotones --- Convex functions. --- Differentiable functions. --- Monotone operators. --- Fonctions différentiables --- Opérateurs monotones --- 517.17 --- 517.518 --- Basic properties of functions. Continuity. Monotonicity etc. --- Metric theory of functions --- 517.518 Metric theory of functions --- 517.17 Basic properties of functions. Continuity. Monotonicity etc. --- Operator theory --- Analyse fonctionnelle non linéaire --- Nonlinear functional analysis --- Analyse fonctionnelle non linéaire. --- Analyse fonctionnelle non linéaire.
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In this new edition of LNM 1693 the essential idea is to reduce questions on monotone multifunctions to questions on convex functions. However, rather than using a “big convexification” of the graph of the multifunction and the “minimax technique”for proving the existence of linear functionals satisfying certain conditions, the Fitzpatrick function is used. The journey begins with a generalization of the Hahn-Banach theorem uniting classical functional analysis, minimax theory, Lagrange multiplier theory and convex analysis and culminates in a survey of current results on monotone multifunctions on a Banach space. The first two chapters are aimed at students interested in the development of the basic theorems of functional analysis, which leads painlessly to the theory of minimax theorems, convex Lagrange multiplier theory and convex analysis. The remaining five chapters are useful for those who wish to learn about the current research on monotone multifunctions on (possibly non reflexive) Banach space.
Monotone operators. --- Monotonic functions. --- Banach spaces. --- Opérateurs monotones --- Fonctions monotones --- Banach, Espaces de --- Monotone operators --- Monotonic functions --- Banach spaces --- Duality theory (Mathematics) --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Maxima and minima. --- Opérateurs monotones --- EPUB-LIV-FT SPRINGER-B --- Functions, Monotonic --- Minima --- Mathematics. --- Functional analysis. --- Operator theory. --- Calculus of variations. --- Functional Analysis. --- Calculus of Variations and Optimal Control; Optimization. --- Operator Theory. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Functional analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Math --- Science --- Functions of real variables --- Operator theory --- Algebra --- Mathematical analysis --- Topology --- Functions of complex variables --- Generalized spaces --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Operations research --- Simulation methods --- System analysis
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This book presents a largely self-contained account of the main results of convex analysis, monotone operator theory, and the theory of nonexpansive operators in the context of Hilbert spaces. Unlike existing literature, the novelty of this book, and indeed its central theme, is the tight interplay among the key notions of convexity, monotonicity, and nonexpansiveness. The presentation is accessible to a broad audience and attempts to reach out in particular to the applied sciences and engineering communities, where these tools have become indispensable. Graduate students and researchers in pure and applied mathematics will benefit from this book. It is also directed to researchers in engineering, decision sciences, economics, and inverse problems, and can serve as a reference book. Author Information: Heinz H. Bauschke is a Professor of Mathematics at the University of British Columbia, Okanagan campus (UBCO) and currently a Canada Research Chair in Convex Analysis and Optimization. He was born in Frankfurt where he received his "Diplom-Mathematiker (mit Auszeichnung)" from Goethe Universität in 1990. He defended his Ph.D. thesis in Mathematics at Simon Fraser University in 1996 and was awarded the Governor General's Gold Medal for his graduate work. After a NSERC Postdoctoral Fellowship spent at the University of Waterloo, at the Pennsylvania State University, and at the University of California at Santa Barbara, Dr. Bauschke became College Professor at Okanagan University College in 1998. He joined the University of Guelph in 2001, and he returned to Kelowna in 2005, when Okanagan University College turned into UBCO. In 2009, he became UBCO's first "Researcher of the Year". Patrick L. Combettes received the Brevet d'Études du Premier Cycle from Académie de Versailles in 1977 and the Ph.D. degree from North Carolina State University in 1989. In 1990, he joined the City College and the Graduate Center of the City University of New York where he became a Full Professor in 1999. Since 1999, he has been with the Faculty of Mathematics of Université Pierre et Marie Curie -- Paris 6, laboratoire Jacques-Louis Lions, where he is presently a Professeur de Classe Exceptionnelle. He was elected Fellow of the IEEE in 2005.
Numerical methods of optimisation --- Computer science --- Computer architecture. Operating systems --- visualisatie --- algoritmen --- kansrekening --- optimalisatie --- Hilbert space --- Nonlinear functional analysis --- Monotone operators --- Espace de Hilbert --- Analyse fonctionnelle non linéaire --- Opérateurs monotones --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Hilbert space. --- Approximation theory. --- Monotone operators. --- Nonlinear functional analysis. --- Functional analysis --- Nonlinear theories --- Operator theory --- Theory of approximation --- Functions --- Polynomials --- Chebyshev systems --- Banach spaces --- Hyperspace --- Inner product spaces --- Approximation theory --- Calculus of variations. --- Algorithms. --- Mathematics. --- Visualization. --- Calculus of Variations and Optimal Control; Optimization. --- Math --- Science --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Visualisation --- Imagination --- Visual perception --- Imagery (Psychology) --- Algorism --- Algebra --- Arithmetic --- Foundations
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Hilbert space. --- Monotone operators. --- Semigroups. --- Group theory --- Operator theory --- Banach spaces --- Hyperspace --- Inner product spaces --- Monotone operators --- Semigroups --- Hilbert space --- Opérateurs monotones --- Semi-groupes --- Espace de Hilbert --- ELSEVIER-B EPUB-LIV-FT --- Nonlinear functional analysis --- Analyse fonctionnelle non linéaire. --- Nonlinear functional analysis. --- Analyse fonctionnelle non linéaire --- Differential equations --- 517.9 --- 517.9 Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- Differential equations. Integral equations. Other functional equations. Finite differences. Calculus of variations. Functional analysis --- 517.91 --- 517.91 Ordinary differential equations: general theory --- Ordinary differential equations: general theory --- Operateurs hilbertiens
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Functional analysis --- Monotonic functions --- Maxima and minima --- Duality theory (Mathematics) --- Monotone operators --- Calculus --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Dualiteit [Theorie van de ] (Wiskunde) --- Dualité [Théorie de la ] (Mathématiques) --- Fonctions monotones --- Functies [Monotoon ] --- Functions [Monotonic ] --- Mathematics duality theory --- Maxima en minima --- Maxima et minima --- Monotone functies --- Monotone operatoren --- Opérateurs monotones --- Theorie van de dualiteit (Wiskunde) --- Théorie de la dualité (Mathématiques) --- Opérateurs monotones --- Dualité, Principe de (Mathématiques) --- Functional analysis. --- Operator theory. --- System theory. --- Calculus of variations. --- Functional Analysis. --- Operator Theory. --- Systems Theory, Control. --- Calculus of Variations and Optimal Control; Optimization. --- Isoperimetrical problems --- Variations, Calculus of --- Systems, Theory of --- Systems science --- Science --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Philosophy --- Monotone operators. --- Algebra --- Mathematical analysis --- Topology --- Operator theory
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Devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure, this book focuses on gradient flows in metric spaces. It covers gradient flows in the space of probability measures on a separable Hilbert space, endowed with the Kantorovich-Rubinstein-Wasserstein distance.
Differential geometry. Global analysis --- Mathematical physics --- Operational research. Game theory --- differentiaalvergelijkingen --- kansrekening --- differentiaal geometrie --- stochastische analyse --- Measure theory --- Metric spaces --- Differential equations, Partial --- Monotone operators --- Evolution equations, Nonlinear --- Mesure, Théorie de la --- Espaces métriques --- Equations aux dérivées partielles --- Opérateurs monotones --- Equations d'évolution non linéaires --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Global analysis (Mathematics). --- Mathematics. --- Global differential geometry. --- Distribution (Probability theory. --- Analysis. --- Measure and Integration. --- Differential Geometry. --- Probability Theory and Stochastic Processes. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Geometry, Differential --- Math --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Mathematical analysis. --- Analysis (Mathematics). --- Measure theory. --- Differential geometry. --- Probabilities. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Differential geometry --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- 517.1 Mathematical analysis --- Mathematical analysis --- Metric spaces. --- Differential equations, Parabolic. --- Monotone operators. --- Evolution equations, Nonlinear. --- Operator theory --- Parabolic differential equations --- Parabolic partial differential equations --- Spaces, Metric --- Generalized spaces --- Set theory --- Topology --- Nonlinear equations of evolution --- Nonlinear evolution equations --- Differential equations, Nonlinear
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