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Optimization in Function Spaces: With Stability Considerations in Orlicz Spaces, Kosmol Peter, Mьller-Wichards Dieter


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Автор: Kosmol Peter, Mьller-Wichards Dieter
Название:  Optimization in Function Spaces: With Stability Considerations in Orlicz Spaces
ISBN: 9783110250206
Издательство: Walter de Gruyter
Издательство: de Gruyter
Классификация:
ISBN-10: 3110250209
Обложка/Формат: Hardcover
Страницы: 402
Вес: 0.84 кг.
Дата издания: 17.02.2011
Серия: De gruyter series in nonlinear analysis & applications
Язык: English
Размер: 24.41 x 16.99 x 2.39 cm
Читательская аудитория: Professional & vocational
Подзаголовок: With stability considerations in orlicz spaces
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Поставляется из: США
Описание:

This is an essentially self-contained book on the theory of convex functions and convex optimization in Banach spaces, with a special interest in Orlicz spaces.

Approximate algorithms based on the stability principles and the solution of the corresponding nonlinear equations are developed in this text. A synopsis of the geometry of Banach spaces, aspects of stability and the duality of different levels of differentiability and convexity is developed. A particular emphasis is placed on the geometrical aspects of strong solvability of a convex optimization problem: it turns out that this property is equivalent to local uniform convexity of the corresponding convex function. This treatise also provides a novel approach to the fundamental theorems of Variational Calculus based on the principle of pointwise minimization of the Lagrangian on the one hand and convexification by quadratic supplements using the classical Legendre-Ricatti equation on the other.

The reader should be familiar with the concepts of mathematical analysis and linear algebra. Some awareness of the principles of measure theory will turn out to be helpful. The book is suitable for students of the second half of undergraduate studies, and it provides a rich set of material for a master course on linear and nonlinear functional analysis. Additionally it offers novel aspects at the advanced level.

From the contents:

  • Approximation and Polya Algorithms in Orlicz Spaces
  • Convex Sets and Convex Functions
  • Numerical Treatment of Non-linear Equations and Optimization Problems
  • Stability and Two-stage Optimization Problems
  • Orlicz Spaces, Orlicz Norm and Duality
  • Differentiability and Convexity in Orlicz Spaces
  • Variational Calculus



Optimization on Metric and Normed Spaces

Автор: Alexander Zaslavski
Название: Optimization on Metric and Normed Spaces
ISBN: 0387886206 ISBN-13(EAN): 9780387886206
Издательство: Springer
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Цена: 23058.00 р.
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Описание: Covering recent work on Banach and complete metric spaces, this book uses the Baire approach and considers approximate solutions. It presents new results including penalty methods in constrained optimization and extant solutions in parametric optimization.

Functional Analysis and Applied Optimization in Banach Spaces

Автор: Fabio Botelho
Название: Functional Analysis and Applied Optimization in Banach Spaces
ISBN: 3319060732 ISBN-13(EAN): 9783319060736
Издательство: Springer
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Цена: 16769.00 р.
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Описание: Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one.

Convex analysis and optimization in Hadamard spaces

Автор: Miroslav Bacak
Название: Convex analysis and optimization in Hadamard spaces
ISBN: 3110361035 ISBN-13(EAN): 9783110361032
Издательство: Walter de Gruyter
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Цена: 20446.00 р.
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Описание: In the past two decades, convex analysis and optimization have been developed in Hadamard spaces. This book represents a first attempt to give a systematic account on the subject. Hadamard spaces are complete geodesic spaces of nonpositive curvature. They include Hilbert spaces, Hadamard manifolds, Euclidean buildings and many other important spaces. While the role of Hadamard spaces in geometry and geometric group theory has been studied for a long time, first analytical results appeared as late as in the 1990s. Remarkably, it turns out that Hadamard spaces are appropriate for the theory of convex sets and convex functions outside of linear spaces. Since convexity underpins a large number of results in the geometry of Hadamard spaces, we believe that its systematic study is of substantial interest. Optimization methods then address various computational issues and provide us with approximation algorithms which may be useful in sciences and engineering. We present a detailed description of such an application to computational phylogenetics. The book is primarily aimed at both graduate students and researchers in analysis and optimization, but it is accessible to advanced undergraduate students as well.

Functional analysis and applied optimization in banach spaces

Автор: Botelho, Fabio
Название: Functional analysis and applied optimization in banach spaces
ISBN: 3319382063 ISBN-13(EAN): 9783319382067
Издательство: Springer
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Цена: 15372.00 р.
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Описание: Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one.

Fixed Point Theory in Modular Function Spaces

Автор: Mohamed A. Khamsi; Wojciech M. Kozlowski
Название: Fixed Point Theory in Modular Function Spaces
ISBN: 3319140507 ISBN-13(EAN): 9783319140506
Издательство: Springer
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Цена: 11878.00 р.
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Описание: This monograph provides a concise introduction to the main results and methods of the fixed point theory in modular function spaces.

Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science

Автор: Isaac Pesenson; Quoc Thong Le Gia; Azita Mayeli; H
Название: Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science
ISBN: 3319555553 ISBN-13(EAN): 9783319555553
Издательство: Springer
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Цена: 16769.00 р.
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Описание: Introduction.- Characterization of Gevrey Regularity by a Class of FBI Transforms.- A Novel Mathematical Approach to the Theory of Translation Invariant Linear Systems.- Asymptotic Behaviour of the Fourier Transform of a Function of Bounded Variation.- Convergence and Regularization of Sampling Series.- Harmonic Analysis in Non-Euclidean Spaces: Theory and Application.- An Harmonic Analysis of Directed Graphs from Arithmetic Functions and Primes.- Sheaf and Duality Methods for Analyzing Multi-Model Systems.- On Boundary-Value Problems for a Partial Differential Equation with Caputo and Bessel Operator.- On the Solvability of the Zaremba Problem in Infinite Sectors and the Invertibility of Associated Singular Integral Operators.- On the Solution of the Oblique Derivative Problem by Constructive Runge-Walsh Concepts.- An Overview of Numerical Acceleration Techniques for Non-Linear Dimension Reduction.- Adaptive Density Estimation on the Circle by Nearly-Tight Frames.- Interactions between Kernels, Frames, and Persistent Homology.- Multi-Penalty Regularization for Detecting Relevant Variables.- Stable Likelihood Computation for Gaussian Random Fields.

Orlicz Spaces and Generalized Orlicz Spaces

Автор: Petteri Harjulehto; Peter H?st?
Название: Orlicz Spaces and Generalized Orlicz Spaces
ISBN: 3030150992 ISBN-13(EAN): 9783030150990
Издательство: Springer
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Цена: 6288.00 р.
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Описание: This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak–Orlicz spaces) with minimal assumptions on the generating ?-function. It introduces and develops a technique centered on the use of equivalent ?-functions. Results from classical functional analysis are presented in detail and new material is included on harmonic analysis. Extrapolation is used to prove, for example, the boundedness of Calder?n–Zygmund operators. Finally, central results are provided for Sobolev spaces, including Poincar? and Sobolev–Poincar? inequalities in norm and modular forms.Primarily aimed at researchers and PhD students interested in Orlicz spaces or generalized Orlicz spaces, this book can be used as a basis for advanced graduate courses in analysis.

Convexity and optimization in Banach spaces

Автор: V. Barbu; Th. Precupanu
Название: Convexity and optimization in Banach spaces
ISBN: 9401029202 ISBN-13(EAN): 9789401029209
Издательство: Springer
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Цена: 12157.00 р.
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Описание: It was our intention to make the book seIf-contained and accessible to a large number of readerso To achieve this in Chapter I we have summarized with or without proofs some basic results in functional analysis and non-linear operator equations in Banach spaces. The list of references is not intended to be complete. It refers only to papers which were used or are directly connected with the subjects treated in this book. V. BARBU Jassy, July 1974 TH. PRECUPANU x Pre tace to the English edition This English edition differs from the Romanian version in that several ehanges have been made. Several seetions in Chapters III and IV have been entirely rewritten and several errors and inaccuracies in the first edition were correeted. The authors wish to express their gratitude to Dr. V. Popescu, from the Jassy University, who kindly assisted them in reading various parts of the manuseript, eorreeting errors and improv- ing the presentation.

Analysis of Operators on Function Spaces: The Serguei Shimorin Memorial Volume

Автор: Aleman Alexandru, Hedenmalm Haakan, Khavinson Dmitry
Название: Analysis of Operators on Function Spaces: The Serguei Shimorin Memorial Volume
ISBN: 3030146421 ISBN-13(EAN): 9783030146429
Издательство: Springer
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Цена: 16769.00 р.
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Описание: This book contains both expository articles and original research in the areas of function theory and operator theory. The book is intended for all researchers in the fields of function theory, operator theory and complex analysis in one or several variables.

Frames and Other Bases in Abstract and Function Spaces

Автор: Isaac Pesenson; Quoc Thong Le Gia; Azita Mayeli; H
Название: Frames and Other Bases in Abstract and Function Spaces
ISBN: 3319555499 ISBN-13(EAN): 9783319555492
Издательство: Springer
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Цена: 16769.00 р.
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Описание: Frames: Theory and Practice.- Dynamical Sampling and Systems from Iterative Actions of Operators.- Optimization Methods for Frame Conditioning and Application to Graph Laplacian Scaling.- A Guide to Localized Frames and Applications to Galerkin-Like Representations of Operators.- Computing the Distance between Frames and between Subspaces of a Hilbert Space.- Sigma-Delta Quantization for Fusion Frames and Distributed Sensor Networks.- Recent Progress in Shearlet Theory: Systematic Construction of Shearlet Dilation Groups, Characterization of Wavefront Sets, and New Embeddings.- Numerical Solution to an Energy Concentration Problem Associated with the Special Affine Fourier Transformation.- A Frame Reconstruction Algorithm with Applications to Magnetic Resonance Imaging.- Frame Properties of Shifts of Prolate and Bandpass Prolate Functions.- Fast Fourier Transforms for Spherical Gauss-Laguerre Basis Functions.- Multiscale Radial Basis Functions.- Orthogonal Wavelet Frames on Manifolds Based on Conformal Mappings.- Quasi Monte Carlo Integration and Kernel-Based Function Approximation on Grassmannians.- Construction of Multiresolution Analysis Based on Localized Reproducing Kernels.- Regular Sampling on Metabelian Nilpotent Lie Groups: The Multiplicity-Free Case.- Parseval Space-Frequency Localized Frames on Sub-Riemann Compact Homogeneous Manifolds.

Real-Variable Theory of Musielak-Orlicz Hardy Spaces

Автор: Dachun Yang; Yiyu Liang; Luong Dang Ky
Название: Real-Variable Theory of Musielak-Orlicz Hardy Spaces
ISBN: 3319543601 ISBN-13(EAN): 9783319543604
Издательство: Springer
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Цена: 9083.00 р.
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Описание: The main purpose of this book is to give a detailed and complete survey of recent progress related to the real-variable theory of Musielak-Orlicz Hardy-type function spaces, and to lay the foundations for further applications.The real-variable theory of function spaces has always been at the core of harmonic analysis.

Partial Differential Equations in Anisotropic Musielak-Orlicz Spaces

Автор: Chlebicka Iwona, Gwiazda Piotr, Świerczewska-Gwiazda Agnieszka
Название: Partial Differential Equations in Anisotropic Musielak-Orlicz Spaces
ISBN: 303088855X ISBN-13(EAN): 9783030888558
Издательство: Springer
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Цена: 18167.00 р.
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Описание: This book provides a detailed study of nonlinear partial differential equations satisfying certain nonstandard growth conditions which simultaneously extend polynomial, inhomogeneous and fully anisotropic growth.


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