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Optimization By Vector Space Methods

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Optimization By Vector Space Methods

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Author : David G. Luenberger
language : en
Publisher: John Wiley & Sons
Release Date : 1997-01-23

Optimization By Vector Space Methods written by David G. Luenberger and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-23 with Technology & Engineering categories.

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.

Optimization By Vector Space Methods

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Author : David G. Luenberger
language : en
Publisher: John Wiley & Sons
Release Date : 1997-01-23

First Order Methods In Optimization

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Author : Amir Beck
language : en
Publisher: SIAM
Release Date : 2017-10-02

First Order Methods In Optimization written by Amir Beck and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-02 with Mathematics categories.

The primary goal of this book is to provide a self-contained, comprehensive study of the main ?rst-order methods that are frequently used in solving large-scale problems. First-order methods exploit information on values and gradients/subgradients (but not Hessians) of the functions composing the model under consideration. With the increase in the number of applications that can be modeled as large or even huge-scale optimization problems, there has been a revived interest in using simple methods that require low iteration cost as well as low memory storage. The author has gathered, reorganized, and synthesized (in a unified manner) many results that are currently scattered throughout the literature, many of which cannot be typically found in optimization books. First-Order Methods in Optimization offers comprehensive study of first-order methods with the theoretical foundations; provides plentiful examples and illustrations; emphasizes rates of convergence and complexity analysis of the main first-order methods used to solve large-scale problems; and covers both variables and functional decomposition methods.

From Vector Spaces To Function Spaces

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Author : Yutaka Yamamoto
language : en
Publisher: SIAM
Release Date : 2012-01-01

From Vector Spaces To Function Spaces written by Yutaka Yamamoto and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-01 with Mathematics categories.

This book provides a treatment of analytical methods of applied mathematics. It starts with a review of the basics of vector spaces and brings the reader to an advanced discussion of applied mathematics, including the latest applications to systems and control theory. The text is designed to be accessible to those not familiar with the material and useful to working scientists, engineers, and mathematics students. The author provides the motivations of definitions and the ideas underlying proofs but does not sacrifice mathematical rigor. From Vector Spaces to Function Spaces presents: an easily accessible discussion of analytical methods of applied mathematics from vector spaces to distributions, Fourier analysis, and Hardy spaces with applications to system theory; an introduction to modern functional analytic methods to better familiarize readers with basic methods and mathematical thinking; and an understandable yet penetrating treatment of such modern methods and topics as function spaces and distributions, Fourier and Laplace analyses, and Hardy spaces.

Vector Optimization With Infimum And Supremum

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Author : Andreas Löhne
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-25

Vector Optimization With Infimum And Supremum written by Andreas Löhne and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-25 with Business & Economics categories.

The theory of Vector Optimization is developed by a systematic usage of infimum and supremum. In order to get existence and appropriate properties of the infimum, the image space of the vector optimization problem is embedded into a larger space, which is a subset of the power set, in fact, the space of self-infimal sets. Based on this idea we establish solution concepts, existence and duality results and algorithms for the linear case. The main advantage of this approach is the high degree of analogy to corresponding results of Scalar Optimization. The concepts and results are used to explain and to improve practically relevant algorithms for linear vector optimization problems.

Optimization

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Author : Jan Brinkhuis
language : en
Publisher: Princeton University Press
Release Date : 2005-09-18

Optimization written by Jan Brinkhuis and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-18 with Business & Economics categories.

This self-contained textbook is an informal introduction to optimization through the use of numerous illustrations and applications. The focus is on analytically solving optimization problems with a finite number of continuous variables. In addition, the authors provide introductions to classical and modern numerical methods of optimization and to dynamic optimization. The book's overarching point is that most problems may be solved by the direct application of the theorems of Fermat, Lagrange, and Weierstrass. The authors show how the intuition for each of the theoretical results can be supported by simple geometric figures. They include numerous applications through the use of varied classical and practical problems. Even experts may find some of these applications truly surprising. A basic mathematical knowledge is sufficient to understand the topics covered in this book. More advanced readers, even experts, will be surprised to see how all main results can be grounded on the Fermat-Lagrange theorem. The book can be used for courses on continuous optimization, from introductory to advanced, for any field for which optimization is relevant.

Convex Analysis In General Vector Spaces

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Author : C Zalinescu
language : en
Publisher: World Scientific
Release Date : 2002-07-30

Convex Analysis In General Vector Spaces written by C Zalinescu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-30 with Mathematics categories.

The primary aim of this book is to present the conjugate and subdifferential calculus using the method of perturbation functions in order to obtain the most general results in this field. The secondary aim is to provide important applications of this calculus and of the properties of convex functions. Such applications are: the study of well-conditioned convex functions, uniformly convex and uniformly smooth convex functions, best approximation problems, characterizations of convexity, the study of the sets of weak sharp minima, well-behaved functions and the existence of global error bounds for convex inequalities, as well as the study of monotone multifunctions by using convex functions.

Lectures On Modern Convex Optimization

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Author : Aharon Ben-Tal
language : fr
Publisher: SIAM
Release Date : 2001-01-01

Lectures On Modern Convex Optimization written by Aharon Ben-Tal and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Technology & Engineering categories.

Here is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming. The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design. The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book's focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide spectrum of important optimization problems arising in applications.

Vector Optimization

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Author : Johannes Jahn
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-22

Vector Optimization written by Johannes Jahn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-22 with Business & Economics categories.

Fundamentals and important results of vector optimization in a general setting are presented in this book. The theory developed includes scalarization, existence theorems, a generalized Lagrange multiplier rule and duality results. Applications to vector approximation, cooperative game theory and multiobjective optimization are described. The theory is extended to set optimization with particular emphasis on contingent epiderivatives, subgradients and optimality conditions. Background material of convex analysis being necessary is concisely summarized at the beginning. This second edition contains new parts on the adaptive Eichfelder-Polak method, a concrete application to magnetic resonance systems in medical engineering and additional remarks on the contribution of F.Y. Edgeworth and V. Pareto. The bibliography is updated and includes more recent important publications.

Optimization In Function Spaces

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Author : Amol Sasane
language : en
Publisher: Courier Dover Publications
Release Date : 2016-04-10

Optimization In Function Spaces written by Amol Sasane and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-10 with Mathematics categories.

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 By Vector Space Methods

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