Functional Analysis And Continuous Optimization

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Functional Analysis And Continuous Optimization

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Author : José M. Amigó
language : en
Publisher: Springer Nature
Release Date : 2023-07-01

Functional Analysis And Continuous Optimization written by José M. Amigó and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-01 with Mathematics categories.

The book includes selected contributions presented at the "International Meeting on Functional Analysis and Continuous Optimization" held in Elche (Spain) on June 16–17, 2022. Its contents cover very recent results in functional analysis, continuous optimization and the interplay between these disciplines. Therefore, this book showcases current research on functional analysis and optimization with individual contributions, as well as new developments in both areas. As a result, the reader will find useful information and stimulating ideas.

Functional Analysis And Continuous Optimization

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Author : José M. Amigó
language : en
Publisher:
Release Date : 2023

Functional Analysis And Continuous Optimization written by José M. Amigó and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.

The book includes selected contributions presented at the "International Meeting on Functional Analysis and Continuous Optimization" held in Elche (Spain) on June 16-17, 2022. Its contents cover very recent results in functional analysis, continuous optimization and the interplay between these disciplines. Therefore, this book showcases current research on functional analysis and optimization with individual contributions, as well as new developments in both areas. As a result, the reader will find useful information and stimulating ideas.

Perturbation Analysis Of Optimization Problems

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Author : J.Frederic Bonnans
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-22

Perturbation Analysis Of Optimization Problems written by J.Frederic Bonnans 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 2013-11-22 with Mathematics categories.

The main subject of this book is perturbation analysis of continuous optimization problems. In the last two decades considerable progress has been made in that area, and it seems that it is time now to present a synthetic view of many important results that apply to various classes of problems. The model problem that is considered throughout the book is of the form (P) Min/(x) subjectto G(x) E K. xeX Here X and Y are Banach spaces, K is a closed convex subset of Y, and / : X -+ IR and G : X -+ Y are called the objective function and the constraint mapping, respectively. We also consider a parameteriZed version (P ) of the above u problem, where the objective function / (x, u) and the constraint mapping G(x, u) are parameterized by a vector u varying in a Banach space U. Our aim is to study continuity and differentiability properties of the optimal value v(u) and the set S(u) of optimal solutions of (P ) viewed as functions of the parameter vector u.

Global Optimization In Action

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Author : János D. Pintér
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

Global Optimization In Action written by János D. Pintér 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 2013-03-14 with Mathematics categories.

In science, engineering and economics, decision problems are frequently modelled by optimizing the value of a (primary) objective function under stated feasibility constraints. In many cases of practical relevance, the optimization problem structure does not warrant the global optimality of local solutions; hence, it is natural to search for the globally best solution(s). Global Optimization in Action provides a comprehensive discussion of adaptive partition strategies to solve global optimization problems under very general structural requirements. A unified approach to numerous known algorithms makes possible straightforward generalizations and extensions, leading to efficient computer-based implementations. A considerable part of the book is devoted to applications, including some generic problems from numerical analysis, and several case studies in environmental systems analysis and management. The book is essentially self-contained and is based on theauthor's research, in cooperation (on applications) with a number of colleagues. Audience: Professors, students, researchers and other professionals in the fields of operations research, management science, industrial and applied mathematics, computer science, engineering, economics and the environmental sciences.

Linear Semi Infinite Optimization

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Author : Miguel A. Goberna
language : en
Publisher:
Release Date : 1998-03-11

Linear Semi Infinite Optimization written by Miguel A. Goberna and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-03-11 with Mathematics categories.

A linear semi-infinite program is an optimization problem with linear objective functions and linear constraints in which either the number of unknowns or the number of constraints is finite. The many direct applications of linear semi-infinite optimization (or programming) have prompted considerable and increasing research effort in recent years. The authors' aim is to communicate the main theoretical ideas and applications techniques of this fascinating area, from the perspective of convex analysis. The four sections of the book cover: * Modelling with primal and dual problems - the primal problem, space of dual variables, the dual problem. * Linear semi-infinite systems - existence theorems, alternative theorems, redundancy phenomena, geometrical properties of the solution set. * Theory of linear semi-infinite programming - optimality, duality, boundedness, perturbations, well-posedness. * Methods of linear semi-infinite programming - an overview of the main numerical methods for primal and dual problems. Exercises and examples are provided to illustrate both theory and applications. The reader is assumed to be familiar with elementary calculus, linear algebra and general topology. An appendix on convex analysis is provided to ensure that the book is self-contained. Graduate students and researchers wishing to gain a deeper understanding of the main ideas behind the theory of linear optimization will find this book to be an essential text.

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.

Convex Optimization

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Author : Stephen P. Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2004-03-08

Convex Optimization written by Stephen P. Boyd and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-08 with Business & Economics categories.

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.

A Mathematical View Of Interior Point Methods In Convex Optimization

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Author : James Renegar
language : en
Publisher: SIAM
Release Date : 2001-01-01

A Mathematical View Of Interior Point Methods In Convex Optimization written by James Renegar 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 Mathematics 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.

Functional Analysis Calculus Of Variations And Optimal Control

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Author : Francis Clarke
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-02-06

Functional Analysis Calculus Of Variations And Optimal Control written by Francis Clarke 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 2013-02-06 with Mathematics categories.

Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.

Functional Analysis

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Author : N.B. Singh
language : en
Publisher: N.B. Singh
Release Date :

Functional Analysis written by N.B. Singh and has been published by N.B. Singh this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

This book, Functional Analysis, is designed for absolute beginners who want to understand the fundamental ideas of functional analysis without advanced prerequisites. Starting from the basics, it introduces concepts like vector spaces, norms, and linear operators, using simple explanations and examples to build a strong foundation. Each chapter breaks down complex topics step-by-step, making it accessible for anyone new to the subject. By the end, readers will have a clear understanding of the core principles of functional analysis and how these ideas apply in mathematics, physics, and engineering.