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Optimization In Banach Spaces

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Convexity And Optimization In Banach Spaces

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Author : Viorel Barbu
language : ro
Publisher: Springer
Release Date : 1978

Convexity And Optimization In Banach Spaces written by Viorel Barbu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Juvenile Nonfiction categories.

Convexity And Optimization In Banach Spaces

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Author : Viorel Barbu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-03

Convexity And Optimization In Banach Spaces written by Viorel Barbu 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 2012-01-03 with Mathematics categories.

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.

Optimization In Banach Spaces

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Author : Alexander J. Zaslavski
language : en
Publisher: Springer Nature
Release Date : 2022-09-29

Optimization In Banach Spaces written by Alexander J. Zaslavski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-29 with Mathematics categories.

The book is devoted to the study of constrained minimization problems on closed and convex sets in Banach spaces with a Frechet differentiable objective function. Such problems are well studied in a finite-dimensional space and in an infinite-dimensional Hilbert space. When the space is Hilbert there are many algorithms for solving optimization problems including the gradient projection algorithm which is one of the most important tools in the optimization theory, nonlinear analysis and their applications. An optimization problem is described by an objective function and a set of feasible points. For the gradient projection algorithm each iteration consists of two steps. The first step is a calculation of a gradient of the objective function while in the second one we calculate a projection on the feasible set. In each of these two steps there is a computational error. In our recent research we show that the gradient projection algorithm generates a good approximate solution, if all the computational errors are bounded from above by a small positive constant. It should be mentioned that the properties of a Hilbert space play an important role. When we consider an optimization problem in a general Banach space the situation becomes more difficult and less understood. On the other hand such problems arise in the approximation theory. The book is of interest for mathematicians working in optimization. It also can be useful in preparation courses for graduate students. The main feature of the book which appeals specifically to this audience is the study of algorithms for convex and nonconvex minimization problems in a general Banach space. The book is of interest for experts in applications of optimization to the approximation theory. In this book the goal is to obtain a good approximate solution of the constrained optimization problem in a general Banach space under the presence of computational errors. It is shown that the algorithm generates a good approximate solution, if the sequence of computational errors is bounded from above by a small constant. The book consists of four chapters. In the first we discuss several algorithms which are studied in the book and prove a convergence result for an unconstrained problem which is a prototype of our results for the constrained problem. In Chapter 2 we analyze convex optimization problems. Nonconvex optimization problems are studied in Chapter 3. In Chapter 4 we study continuous algorithms for minimization problems under the presence of computational errors. The algorithm generates a good approximate solution, if the sequence of computational errors is bounded from above by a small constant. The book consists of four chapters. In the first we discuss several algorithms which are studied in the book and prove a convergence result for an unconstrained problem which is a prototype of our results for the constrained problem. In Chapter 2 we analyze convex optimization problems. Nonconvex optimization problems are studied in Chapter 3. In Chapter 4 we study continuous algorithms for minimization problems under the presence of computational errors.

Optimization In Banach Spaces

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Author : Aleksandr J. Zaslavskij
language : en
Publisher:
Release Date : 2022

Optimization In Banach Spaces written by Aleksandr J. Zaslavskij and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Mathematical optimization categories.

Functional Analysis And Applied Optimization In Banach Spaces

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Author : Fabio Botelho
language : en
Publisher: Springer
Release Date : 2014-06-12

Functional Analysis And Applied Optimization In Banach Spaces written by Fabio Botelho and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-12 with Mathematics categories.

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

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Author : V. Barbu
language : en
Publisher:
Release Date : 2014-08-15

Convexity And Optimization In Banach Spaces written by V. Barbu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-15 with categories.

Convexity And Optimization In Banach Spaces

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Author : Viorel Barbu
language : en
Publisher: Springer
Release Date : 2013-01-02

Convexity And Optimization In Banach Spaces

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Author : V. Barbu
language : en
Publisher: Springer
Release Date : 2014-09-12

Convexity And Optimization In Banach Spaces written by V. Barbu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-12 with Science categories.

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.

Optimization In Banach Spaces

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