Optimization In Function Spaces

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Optimization in Function Spaces

Amol Sasane
Optimization in Function Spaces Book PDF

Author : Amol Sasane
Publisher : Courier Dover Publications
Page : 256 pages
File Size : 45,8 Mb
Release : 2016-04-10
Category : Mathematics
ISBN : 9780486810966

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Optimization in Function Spaces by Amol Sasane Pdf

This highly readable volume on optimization in function spaces is based on author Amol Sasane's lecture notes, which he developed over several years while teaching a course for third-year undergraduates at the London School of Economics. The classroom-tested text is written in an informal but precise style that emphasizes clarity and detail, taking students step by step through each subject. Numerous examples throughout the text clarify methods, and a substantial number of exercises provide reinforcement. Detailed solutions to all of the exercises make this book ideal for self-study. The topics are relevant to students in engineering and economics as well as mathematics majors. Prerequisites include multivariable calculus and basic linear algebra. The necessary background in differential equations and elementary functional analysis is developed within the text, offering students a self-contained treatment.

Optimization in Function Spaces with Stability Considerations in Orlicz Spaces

Peter Kosmol,Dieter Müller-Wichards
Optimization in Function Spaces with Stability Considerations in Orlicz Spaces Book PDF

Author : Peter Kosmol,Dieter Müller-Wichards
Publisher : Walter de Gruyter
Page : 405 pages
File Size : 45,7 Mb
Release : 2011
Category : Mathematics
ISBN : 9783110250206

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Optimization in Function Spaces with Stability Considerations in Orlicz Spaces by Peter Kosmol,Dieter Müller-Wichards Pdf

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 in Function Spaces

Peter Kosmol,Dieter Müller-Wichards
Optimization in Function Spaces Book PDF

Author : Peter Kosmol,Dieter Müller-Wichards
Publisher : Walter de Gruyter
Page : 405 pages
File Size : 52,8 Mb
Release : 2011-02-28
Category : Mathematics
ISBN : 9783110250213

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Optimization in Function Spaces by Peter Kosmol,Dieter Müller-Wichards Pdf

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

Functional Analysis and Applied Optimization in Banach Spaces

Fabio Botelho
Functional Analysis and Applied Optimization in Banach Spaces Book PDF

Author : Fabio Botelho
Publisher : Springer
Page : 584 pages
File Size : 53,7 Mb
Release : 2014-06-12
Category : Mathematics
ISBN : 9783319060743

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Functional Analysis and Applied Optimization in Banach Spaces by Fabio Botelho Pdf

​This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. 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. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.

Convexity and Optimization in Banach Spaces

Viorel Barbu,Teodor Precupanu
Convexity and Optimization in Banach Spaces Book PDF

Author : Viorel Barbu,Teodor Precupanu
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 52,9 Mb
Release : 2012-01-03
Category : Mathematics
ISBN : 9789400722460

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Convexity and Optimization in Banach Spaces by Viorel Barbu,Teodor Precupanu Pdf

An updated and revised edition of the 1986 title Convexity and Optimization in Banach Spaces, this book provides a self-contained presentation of basic results of the theory of convex sets and functions in infinite-dimensional spaces. The main emphasis is on applications to convex optimization and convex optimal control problems in Banach spaces. A distinctive feature is a strong emphasis on the connection between theory and application. This edition has been updated to include new results pertaining to advanced concepts of subdifferential for convex functions and new duality results in convex programming. The last chapter, concerned with convex control problems, has been rewritten and completed with new research concerning boundary control systems, the dynamic programming equations in optimal control theory and periodic optimal control problems. Finally, the structure of the book has been modified to highlight the most recent progression in the field including fundamental results on the theory of infinite-dimensional convex analysis and includes helpful bibliographical notes at the end of each chapter.

Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces

Michael Ulbrich
Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces Book PDF

Author : Michael Ulbrich
Publisher : SIAM
Page : 322 pages
File Size : 47,7 Mb
Release : 2011-01-01
Category : Constrained optimization
ISBN : 1611970695

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Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces by Michael Ulbrich Pdf

Semismooth Newton methods are a modern class of remarkably powerful and versatile algorithms for solving constrained optimization problems with partial differential equations (PDEs), variational inequalities, and related problems. This book provides a comprehensive presentation of these methods in function spaces, striking a balance between thoroughly developed theory and numerical applications. Although largely self-contained, the book also covers recent developments in the field, such as state-constrained problems, and offers new material on topics such as improved mesh independence results. The theory and methods are applied to a range of practically important problems, including: optimal control of nonlinear elliptic differential equations, obstacle problems, and flow control of instationary Navier-Stokes fluids. In addition, the author covers adjoint-based derivative computation and the efficient solution of Newton systems by multigrid and preconditioned iterative methods.

Convex Optimization in Normed Spaces

Juan Peypouquet
Convex Optimization in Normed Spaces Book PDF

Author : Juan Peypouquet
Publisher : Springer
Page : 124 pages
File Size : 52,9 Mb
Release : 2015-03-18
Category : Mathematics
ISBN : 9783319137100

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Convex Optimization in Normed Spaces by Juan Peypouquet Pdf

This work is intended to serve as a guide for graduate students and researchers who wish to get acquainted with the main theoretical and practical tools for the numerical minimization of convex functions on Hilbert spaces. Therefore, it contains the main tools that are necessary to conduct independent research on the topic. It is also a concise, easy-to-follow and self-contained textbook, which may be useful for any researcher working on related fields, as well as teachers giving graduate-level courses on the topic. It will contain a thorough revision of the extant literature including both classical and state-of-the-art references.

Optimization by Vector Space Methods

David G. Luenberger
Optimization by Vector Space Methods Book PDF

Author : David G. Luenberger
Publisher : John Wiley & Sons
Page : 348 pages
File Size : 44,9 Mb
Release : 1997-01-23
Category : Technology & Engineering
ISBN : 047118117X

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Optimization by Vector Space Methods by David G. Luenberger Pdf

Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book.

Functional Analysis, Sobolev Spaces and Partial Differential Equations

Haim Brezis
Functional Analysis Sobolev Spaces and Partial Differential Equations Book PDF

Author : Haim Brezis
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 53,5 Mb
Release : 2010-11-02
Category : Mathematics
ISBN : 9780387709147

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Functional Analysis, Sobolev Spaces and Partial Differential Equations by Haim Brezis Pdf

This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.

Optimization on Metric and Normed Spaces

Alexander Zaslavski
Optimization on Metric and Normed Spaces Book PDF

Author : Alexander Zaslavski
Publisher : Springer
Page : 0 pages
File Size : 41,6 Mb
Release : 2012-10-13
Category : Mathematics
ISBN : 1461426405

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Optimization on Metric and Normed Spaces by Alexander Zaslavski Pdf

"Optimization on Metric and Normed Spaces" is devoted to the recent progress in optimization on Banach spaces and complete metric spaces. Optimization problems are usually considered on metric spaces satisfying certain compactness assumptions which guarantee the existence of solutions and convergence of algorithms. This book considers spaces that do not satisfy such compactness assumptions. In order to overcome these difficulties, the book uses the Baire category approach and considers approximate solutions. Therefore, it presents a number of new results concerning penalty methods in constrained optimization, existence of solutions in parametric optimization, well-posedness of vector minimization problems, and many other results obtained in the last ten years. The book is intended for mathematicians interested in optimization and applied functional analysis.

Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization

D. Butnariu,A.N. Iusem
Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization Book PDF

Author : D. Butnariu,A.N. Iusem
Publisher : Springer Science & Business Media
Page : 218 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401140669

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Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization by D. Butnariu,A.N. Iusem Pdf

The aim of this work is to present in a unified approach a series of results concerning totally convex functions on Banach spaces and their applications to building iterative algorithms for computing common fixed points of mea surable families of operators and optimization methods in infinite dimen sional settings. The notion of totally convex function was first studied by Butnariu, Censor and Reich [31] in the context of the space lRR because of its usefulness for establishing convergence of a Bregman projection method for finding common points of infinite families of closed convex sets. In this finite dimensional environment total convexity hardly differs from strict convexity. In fact, a function with closed domain in a finite dimensional Banach space is totally convex if and only if it is strictly convex. The relevancy of total convexity as a strengthened form of strict convexity becomes apparent when the Banach space on which the function is defined is infinite dimensional. In this case, total convexity is a property stronger than strict convexity but weaker than locally uniform convexity (see Section 1.3 below). The study of totally convex functions in infinite dimensional Banach spaces was started in [33] where it was shown that they are useful tools for extrapolating properties commonly known to belong to operators satisfying demanding contractivity requirements to classes of operators which are not even mildly nonexpansive.

Convex Analysis and Optimization in Hadamard Spaces

Miroslav Bacak
Convex Analysis and Optimization in Hadamard Spaces Book PDF

Author : Miroslav Bacak
Publisher : Walter de Gruyter GmbH & Co KG
Page : 217 pages
File Size : 55,8 Mb
Release : 2014-10-29
Category : Mathematics
ISBN : 9783110391084

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Convex Analysis and Optimization in Hadamard Spaces by Miroslav Bacak Pdf

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.

Function Spaces

Conference on Function Spaces
Function Spaces Book PDF

Author : Conference on Function Spaces
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 43,8 Mb
Release : 2007
Category : Function spaces
ISBN : 9780821840610

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Function Spaces by Conference on Function Spaces Pdf

This book consists of contributions by the participants of the Fifth Conference on Function Spaces, held at Southern Illinois University in May of 2006. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), $L{p $-spaces, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects. The goal of the conference was to bring together mathematicians interested in various problems related to function spaces and to facilitate the exchange of ideas between people working on similar problems. Hence, the majority of papers in this book are accessible to non-experts. Some articles contain expositions of known results and discuss open problems, others contain new results.

Fixed Point Theory, Variational Analysis, and Optimization

Saleh Abdullah R. Al-Mezel,Falleh Rajallah M. Al-Solamy,Qamrul Hasan Ansari
Fixed Point Theory Variational Analysis and Optimization Book PDF

Author : Saleh Abdullah R. Al-Mezel,Falleh Rajallah M. Al-Solamy,Qamrul Hasan Ansari
Publisher : CRC Press
Page : 370 pages
File Size : 50,8 Mb
Release : 2014-06-03
Category : Business & Economics
ISBN : 9781482222074

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Fixed Point Theory, Variational Analysis, and Optimization by Saleh Abdullah R. Al-Mezel,Falleh Rajallah M. Al-Solamy,Qamrul Hasan Ansari Pdf

Fixed Point Theory, Variational Analysis, and Optimization not only covers three vital branches of nonlinear analysis—fixed point theory, variational inequalities, and vector optimization—but also explains the connections between them, enabling the study of a general form of variational inequality problems related to the optimality conditions involving differentiable or directionally differentiable functions. This essential reference supplies both an introduction to the field and a guideline to the literature, progressing from basic concepts to the latest developments. Packed with detailed proofs and bibliographies for further reading, the text: Examines Mann-type iterations for nonlinear mappings on some classes of a metric space Outlines recent research in fixed point theory in modular function spaces Discusses key results on the existence of continuous approximations and selections for set-valued maps with an emphasis on the nonconvex case Contains definitions, properties, and characterizations of convex, quasiconvex, and pseudoconvex functions, and of their strict counterparts Discusses variational inequalities and variational-like inequalities and their applications Gives an introduction to multi-objective optimization and optimality conditions Explores multi-objective combinatorial optimization (MOCO) problems, or integer programs with multiple objectives Fixed Point Theory, Variational Analysis, and Optimization is a beneficial resource for the research and study of nonlinear analysis, optimization theory, variational inequalities, and mathematical economics. It provides fundamental knowledge of directional derivatives and monotonicity required in understanding and solving variational inequality problems.

Function Spaces, 1

Luboš Pick,Alois Kufner,Oldřich John,Svatopluk Fucík
Function Spaces 1 Book PDF

Author : Luboš Pick,Alois Kufner,Oldřich John,Svatopluk Fucík
Publisher : Walter de Gruyter
Page : 495 pages
File Size : 55,7 Mb
Release : 2012-12-19
Category : Mathematics
ISBN : 9783110250428

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Function Spaces, 1 by Luboš Pick,Alois Kufner,Oldřich John,Svatopluk Fucík Pdf

This is the first part of the second revised and extended edition of the well established book "Function Spaces" by Alois Kufner, Oldřich John, and Svatopluk Fučík. Like the first edition this monograph is an introduction to function spaces defined in terms of differentiability and integrability classes. It provides a catalogue of various spaces and benefits as a handbook for those who use function spaces in their research or lecture courses. This first volume is devoted to the study of function spaces, based on intrinsic properties of a function such as its size, continuity, smoothness, various forms of a control over the mean oscillation, and so on. The second volume will be dedicated to the study of function spaces of Sobolev type, in which the key notion is the weak derivative of a function of several variables.