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Approximation And Optimization Of Discrete And Differential Inclusions

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Approximation and Optimization of Discrete and Differential Inclusions

Approximation and Optimization of Discrete and Differential Inclusions Book
Author : Elimhan N Mahmudov
Publisher : Elsevier
Release : 2011-09-08
ISBN : 0123884284
Language : En, Es, Fr & De

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Book Description :

Optimal control theory has numerous applications in both science and engineering. This book presents basic concepts and principles of mathematical programming in terms of set-valued analysis and develops a comprehensive optimality theory of problems described by ordinary and partial differential inclusions. In addition to including well-recognized results of variational analysis and optimization, the book includes a number of new and important ones Includes practical examples

Functional Calculus

Functional Calculus Book
Author : Kamal Shah,Baver Okutmuştur
Publisher : BoD – Books on Demand
Release : 2020-06-17
ISBN : 1838800077
Language : En, Es, Fr & De

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Book Description :

The aim of this book is to present a broad overview of the theory and applications related to functional calculus. The book is based on two main subject areas: matrix calculus and applications of Hilbert spaces. Determinantal representations of the core inverse and its generalizations, new series formulas for matrix exponential series, results on fixed point theory, and chaotic graph operations and their fundamental group are contained under the umbrella of matrix calculus. In addition, numerical analysis of boundary value problems of fractional differential equations are also considered here. In addition, reproducing kernel Hilbert spaces, spectral theory as an application of Hilbert spaces, and an analysis of PM10 fluctuations and optimal control are all contained in the applications of Hilbert spaces. The concept of this book covers topics that will be of interest not only for students but also for researchers and professors in this field of mathematics. The authors of each chapter convey a strong emphasis on theoretical foundations in this book.

Advances in Computational Intelligence Part IV

Advances in Computational Intelligence  Part IV Book
Author : Salvatore Greco,Bernadette Bouchon-Meunier,Giulianella Coletti,Mario Fedrizzi,Benedetto Matarazzo,Ronald R. Yager
Publisher : Springer
Release : 2012-07-23
ISBN : 3642317243
Language : En, Es, Fr & De

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Book Description :

These four volumes (CCIS 297, 298, 299, 300) constitute the proceedings of the 14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012, held in Catania, Italy, in July 2012. The 258 revised full papers presented together with six invited talks were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on fuzzy machine learning and on-line modeling; computing with words and decision making; soft computing in computer vision; rough sets and complex data analysis: theory and applications; intelligent databases and information system; information fusion systems; philosophical and methodological aspects of soft computing; basic issues in rough sets; 40th anniversary of the measures of fuziness; SPS11 uncertainty in profiling systems and applications; handling uncertainty with copulas; formal methods to deal with uncertainty of many-valued events; linguistic summarization and description of data; fuzzy implications: theory and applications; sensing and data mining for teaching and learning; theory and applications of intuitionistic fuzzy sets; approximate aspects of data mining and database analytics; fuzzy numbers and their applications; information processing and management of uncertainty in knowledge-based systems; aggregation functions; imprecise probabilities; probabilistic graphical models with imprecision: theory and applications; belief function theory: basics and/or applications; fuzzy uncertainty in economics and business; new trends in De Finetti's approach; fuzzy measures and integrals; multi criteria decision making; uncertainty in privacy and security; uncertainty in the spirit of Pietro Benvenuti; coopetition; game theory; probabilistic approach.

Nonlinear Analysis and Optimization

Nonlinear Analysis and Optimization Book
Author : Boris S. Mordukhovich,Simeon Reich, Alexander J. Zaslavski
Publisher : American Mathematical Soc.
Release : 2016-02-26
ISBN : 1470417367
Language : En, Es, Fr & De

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Book Description :

This volume contains the proceedings of the IMU/AMS Special Session on Nonlinear Analysis and Optimization, held from June 16-19, 2014, at the Second Joint International Meeting of the Israel Mathematical Union (IMU) and the American Mathematical Society (AMS), Bar-Ilan and Tel-Aviv Universities, Israel, and the Workshop on Nonlinear Analysis and Optimization, held on June 12, 2014, at the Technion-Israel Institute of Technology. The papers in this volume cover many different topics in Nonlinear Analysis and Optimization, including: Taylor domination property for analytic functions in the complex disk, mappings with upper integral bounds for p -moduli, multiple Fourier transforms and trigonometric series in line with Hardy's variation, finite-parameter feedback control for stabilizing damped nonlinear wave equations, implicit Euler approximation and optimization of one-sided Lipschitz differential inclusions, Bolza variational problems with extended-valued integrands on large intervals, first order singular variational problem with nonconvex cost, gradient and extragradient methods for the elasticity imaging inverse problem, discrete approximations of the entropy functional for probability measures on the plane, optimal irrigation scheduling for wheat production, existence of a fixed point of nonexpansive mappings in uniformly convex Banach spaces, strong convergence properties of m-accretive bounded operators, the Reich-Simons convex analytic inequality, nonlinear input-output equilibrium, differential linear-quadratic Nash games with mixed state-control constraints, and excessive revenue models of competitive markets.

Topological Structure of the Solution Set for Evolution Inclusions

Topological Structure of the Solution Set for Evolution Inclusions Book
Author : Yong Zhou,Rong-Nian Wang,Li Peng
Publisher : Springer
Release : 2017-10-31
ISBN : 9811066566
Language : En, Es, Fr & De

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Book Description :

This book systematically presents the topological structure of solution sets and attractability for nonlinear evolution inclusions, together with its relevant applications in control problems and partial differential equations. It provides readers the background material needed to delve deeper into the subject and explore the rich research literature. In addition, the book addresses many of the basic techniques and results recently developed in connection with this theory, including the structure of solution sets for evolution inclusions with m-dissipative operators; quasi-autonomous and non-autonomous evolution inclusions and control systems; evolution inclusions with the Hille-Yosida operator; functional evolution inclusions; impulsive evolution inclusions; and stochastic evolution inclusions. Several applications of evolution inclusions and control systems are also discussed in detail. Based on extensive research work conducted by the authors and other experts over the past four years, the information presented is cutting-edge and comprehensive. As such, the book fills an important gap in the body of literature on the structure of evolution inclusions and its applications.

System Modeling and Optimization

System Modeling and Optimization Book
Author : Adam Korytowski,Maciej Szymkat,Kazimierz Malanowski,Wojciech Mitkowski
Publisher : Springer Science & Business Media
Release : 2009-10-15
ISBN : 3642048013
Language : En, Es, Fr & De

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Book Description :

rd This book constitutes a collection of extended versions of papers presented at the 23 IFIP TC7 Conference on System Modeling and Optimization, which was held in C- cow, Poland, on July 23–27, 2007. It contains 7 plenary and 22 contributed articles, the latter selected via a peer reviewing process. Most of the papers are concerned with optimization and optimal control. Some of them deal with practical issues, e. g. , p- formance-based design for seismic risk reduction, or evolutionary optimization in structural engineering. Many contributions concern optimization of infini- dimensional systems, ranging from a general overview of the variational analysis, through optimization and sensitivity analysis of PDE systems, to optimal control of neutral systems. A significant group of papers is devoted to shape analysis and opti- zation. Sufficient optimality conditions for ODE problems, and stochastic control methods applied to mathematical finance, are also investigated. The remaining papers are on mathematical programming, modeling, and information technology. The conference was the 23rd event in the series of such meetings biennially org- ized under the auspices of the Seventh Technical Committee “Systems Modeling and Optimization” of the International Federation for Information Processing (IFIP TC7).

Variational Analysis and Generalized Differentiation II

Variational Analysis and Generalized Differentiation II Book
Author : Boris S. Mordukhovich
Publisher : Springer Science & Business Media
Release : 2006-03-02
ISBN : 3540312463
Language : En, Es, Fr & De

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Book Description :

Comprehensive and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces Presents numerous applications to problems in the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc.

Modern Methods of Optimization

Modern Methods of Optimization Book
Author : Werner Krabs,Jochem Zowe
Publisher : Springer Science & Business Media
Release : 2013-03-14
ISBN : 3662028514
Language : En, Es, Fr & De

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Book Description :

This volume contains the proceedings of the summer school "Modern Methods of Optimization", held at the Schlof3 Thurnau of the University of Bayreuth, October 1-6, 1990. Like other branches of applied mathematics the area of optimization is undergoing a rapid development since the beginning of the computer age. Optimizaiton methods are of increasing importance for both, science and industry. The aim of the summer school was to present state-of-the-art knowledge by inviting 12 specialists from Op timization (and related fields) to present their areas of activity in the form of survey talks. This volume contains 10 of these presentations in slightly extended form. Most lectures started from an undergraduate level and outlinad the developments up to the latest scientifique achievements. This enabled the audience, consisting of about 45 students and young researchers, to get an excellent overview of the latest trends in Optimization as w~ll as a grasp of the breadth of its potential applications. Equally important to the success of the summer school was the "nonmeasurable" part of the activities inherent in such a summer school. Here the inspiring atmosphere of a place like Thurnau helped to establish numerous contacts between "teachers" and "students". The summer school was organized by the Universitii. t Bayreuth together with the Technische Hochschule Darmstadt and was generously sponsored by the Volkswagen stiftung and the Universitii. tsverein Bayreuth. Their interest in the meeting and their support is hereby gratefully acknowledged.

Large Scale Scientific Computing

Large Scale Scientific Computing Book
Author : Ivan Lirkov
Publisher : Springer Science & Business Media
Release : 2006-02-14
ISBN : 3540319948
Language : En, Es, Fr & De

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Book Description :

This book constitutes the thoroughly refereed post-proceedings of the 5th International Conference on Large-Scale Scientific Computations, LSSC 2005, held in Sozopol, Bulgaria in June 2005. The 75 revised full papers presented together with five invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections.

Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control

Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control Book
Author : Boris S. Mordukhovich,Hector J. Sussmann
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1461384893
Language : En, Es, Fr & De

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Book Description :

This IMA Volume in Mathematics and its Applications NONSMOOTH ANALYSIS AND GEOMETRIC METHODS IN DETERMINISTIC OPTIMAL CONTROL is based on the proceedings of a workshop that was an integral part of the 1992-93 IMA program on "Control Theory. " The purpose of this workshop was to concentrate on powerful mathematical techniques that have been de veloped in deterministic optimal control theory after the basic foundations of the theory (existence theorems, maximum principle, dynamic program ming, sufficiency theorems for sufficiently smooth fields of extremals) were laid out in the 1960s. These advanced techniques make it possible to derive much more detailed information about the structure of solutions than could be obtained in the past, and they support new algorithmic approaches to the calculation of such solutions. We thank Boris S. Mordukhovich and Hector J. Sussmann for organiz ing the workshop and editing the proceedings. We also take this oppor tunity to thank the National Science Foundation and the Army Research Office, whose financial support made the workshop possible. A vner Friedman Willard Miller, Jr. v PREFACE This volume contains the proceedings of the workshop on Nonsmooth Analysis and Geometric Methods in Deterministic Optimal Control held at the Institute for Mathematics and its Applications on February 8-17, 1993 during a special year devoted to Control Theory and its Applications. The workshop-whose organizing committee consisted of V. J urdjevic, B. S. Mordukhovich, R. T. Rockafellar, and H. J.

Trends in Mathematical Optimization

Trends in Mathematical Optimization Book
Author : K.H. Hoffmann
Publisher : Birkhäuser
Release : 2013-03-07
ISBN : 3034892977
Language : En, Es, Fr & De

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Book Description :

This volume contains a collection of 23 papers presented at the 4th French-German Conference on Optimization, hold at Irsee, April 21 - 26, 1986. The conference was aUended by ninety scientists: about one third from France, from Germany and from third countries each. They all contributed to a highly interesting and stimulating meeting. The scientifique program consisted of four survey lectures of a more tutorical character and of 61 contributed papers covering almost all areas of optimization. In addition two informal evening sessions and a plenary discussion on further developments of optimization theory were organized. One of the main aims of the organizers was to indicate and to stress the increasing importance of optimization methods for almost all areas of science and for a fast growing number of industry branches. We hope that the conference approached this goal in a certain degree and managed to continue fruitful discussions between -theory and -applications-. Equally important to the official contributions and lectures is the -nonmeasurable part of activities inherent in such a scientific meeting. Here the charming and inspiring atmosphere of a place like Irsee helped to establish numerous new contacts between the participants and to deepen already existing ones. The conference was sponsored by the Bayerische Kultusministerium, the Deutsche Forschungsgemeinschaft and the Universities of Augsburg and Bayreuth. Their interest in the meeting and their assistance is gratefully acknowledged. We would like to thank the authors for their contributions and the referees for their helpful comments.

System Modeling and Optimization

System Modeling and Optimization Book
Author : Dietmar Hömberg,Fredi Tröltzsch
Publisher : Springer
Release : 2013-02-20
ISBN : 3642360629
Language : En, Es, Fr & De

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Book Description :

This book is a collection of thoroughly refereed papers presented at the 25th IFIP TC 7 Conference on System Modeling and Optimization, held in Dresden, Germany, in September 2011. The 55 revised papers were carefully selected from numerous submissions. They are organized in the following topical sections: control of distributed parameter systems; stochastic optimization and control; stabilization, feedback, and model predictive control; flow control; shape and structural optimization; and applications and control of lumped parameter systems.

Introduction to the Theory of Differential Inclusions

Introduction to the Theory of Differential Inclusions Book
Author : Georgi V. Smirnov
Publisher : American Mathematical Society
Release : 2022-02-22
ISBN : 1470468549
Language : En, Es, Fr & De

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Book Description :

A differential inclusion is a relation of the form $dot x in F(x)$, where $F$ is a set-valued map associating any point $x in R^n$ with a set $F(x) subset R^n$. As such, the notion of a differential inclusion generalizes the notion of an ordinary differential equation of the form $dot x = f(x)$. Therefore, all problems usually studied in the theory of ordinary differential equations (existence and continuation of solutions, dependence on initial conditions and parameters, etc.) can be studied for differential inclusions as well. Since a differential inclusion usually has many solutions starting at a given point, new types of problems arise, such as investigation of topological properties of the set of solutions, selection of solutions with given properties, and many others. Differential inclusions play an important role as a tool in the study of various dynamical processes described by equations with a discontinuous or multivalued right-hand side, occurring, in particular, in the study of dynamics of economical, social, and biological macrosystems. They also are very useful in proving existence theorems in control theory. This text provides an introductory treatment to the theory of differential inclusions. The reader is only required to know ordinary differential equations, theory of functions, and functional analysis on the elementary level. Chapter 1 contains a brief introduction to convex analysis. Chapter 2 considers set-valued maps. Chapter 3 is devoted to the Mordukhovich version of nonsmooth analysis. Chapter 4 contains the main existence theorems and gives an idea of the approximation techniques used throughout the text. Chapter 5 is devoted to the viability problem, i.e., the problem of selection of a solution to a differential inclusion that is contained in a given set. Chapter 6 considers the controllability problem. Chapter 7 discusses extremal problems for differential inclusions. Chapter 8 presents stability theory, and Chapter 9 deals with the stabilization problem.

Approximation of Set Valued Functions

Approximation of Set Valued Functions Book
Author : Nira Dyn,Elza Farkhi,Alona Mokhov
Publisher : World Scientific
Release : 2014-10-30
ISBN : 1783263040
Language : En, Es, Fr & De

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Book Description :

This book is aimed at the approximation of set-valued functions with compact sets in an Euclidean space as values. The interest in set-valued functions is rather new. Such functions arise in various modern areas such as control theory, dynamical systems and optimization. The authors' motivation also comes from the newer field of geometric modeling, in particular from the problem of reconstruction of 3D objects from 2D cross-sections. This is reflected in the focus of this book, which is the approximation of set-valued functions with general (not necessarily convex) sets as values, while previous results on this topic are mainly confined to the convex case. The approach taken in this book is to adapt classical approximation operators and to provide error estimates in terms of the regularity properties of the approximated set-valued functions. Specialized results are given for functions with 1D sets as values. Contents:Scientific Background:On Functions with Values in Metric SpacesOn SetsOn Set-Valued Functions (SVFs)Approximation of SVFs with Images in ℝn:Methods Based on Canonical RepresentationsMethods Based on Minkowski Convex CombinationsMethods Based on the Metric AverageMethods Based on Metric Linear CombinationsMethods Based on Metric SelectionsApproximation of SVFs with Images in ℝ:SVFs with Images in ℝ Multi-Segmental and Topological RepresentationsMethods Based on Topological Representation Readership: Researchers and graduate students in the fields of approximation theory, set-valued analysis, dynamical systems, control and game theory, optimization and geometric modeling. Key Features:This is the only book on the subject of approximation of set-valued functionsIt presents the pioneering work on the approximation of set-valued functions with general (not necessarily convex) sets as valuesThe first author is an internationally known expert in the field of Approximation Theory, the second author is an expert in numerical set-valued and non-smooth analysis. The third author received her PhD recently under the supervision of the first two authors. Many of the results presented in the book are based on her thesisKeywords:Approximation;Set-Valued;Set Operations;Minkowski Sum;Metric Average;Parameterization of Sets;Positive Operators;Metric Spaces;Hausdorff Metric

Differential Equations The Second International Colloquium

Differential Equations  The Second International Colloquium Book
Author : Bainov Drumi D,Covachev Valery
Publisher : World Scientific
Release : 1992-09-30
ISBN : 9814554510
Language : En, Es, Fr & De

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Book Description :

Download Differential Equations The Second International Colloquium book written by Bainov Drumi D,Covachev Valery, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

A Relaxation Based Approach to Optimal Control of Hybrid and Switched Systems

A Relaxation Based Approach to Optimal Control of Hybrid and Switched Systems Book
Author : Vadim Azhmyakov
Publisher : Butterworth-Heinemann
Release : 2019-02-14
ISBN : 012814789X
Language : En, Es, Fr & De

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Book Description :

A Relaxation Based Approach to Optimal Control of Hybrid and Switched Systems proposes a unified approach to effective and numerically tractable relaxation schemes for optimal control problems of hybrid and switched systems. The book gives an overview of the existing (conventional and newly developed) relaxation techniques associated with the conventional systems described by ordinary differential equations. Next, it constructs a self-contained relaxation theory for optimal control processes governed by various types (sub-classes) of general hybrid and switched systems. It contains all mathematical tools necessary for an adequate understanding and using of the sophisticated relaxation techniques. In addition, readers will find many practically oriented optimal control problems related to the new class of dynamic systems. All in all, the book follows engineering and numerical concepts. However, it can also be considered as a mathematical compendium that contains the necessary formal results and important algorithms related to the modern relaxation theory. Illustrates the use of the relaxation approaches in engineering optimization Presents application of the relaxation methods in computational schemes for a numerical treatment of the sophisticated hybrid/switched optimal control problems Offers a rigorous and self-contained mathematical tool for an adequate understanding and practical use of the relaxation techniques Presents an extension of the relaxation methodology to the new class of applied dynamic systems, namely, to hybrid and switched control systems

Differential Equations Chaos and Variational Problems

Differential Equations  Chaos and Variational Problems Book
Author : Vasile Staicu
Publisher : Springer Science & Business Media
Release : 2008-03-12
ISBN : 3764384824
Language : En, Es, Fr & De

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Book Description :

This collection of original articles and surveys written by leading experts in their fields is dedicated to Arrigo Cellina and James A. Yorke on the occasion of their 65th birthday. The volume brings the reader to the border of research in differential equations, a fast evolving branch of mathematics that, besides being a main subject for mathematicians, is one of the mathematical tools most used both by scientists and engineers.

Stochastic Differential Inclusions and Applications

Stochastic Differential Inclusions and Applications Book
Author : Michał Kisielewicz
Publisher : Springer Science & Business Media
Release : 2013-06-12
ISBN : 146146756X
Language : En, Es, Fr & De

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Book Description :

​This book aims to further develop the theory of stochastic functional inclusions and their applications for describing the solutions of the initial and boundary value problems for partial differential inclusions. The self-contained volume is designed to introduce the reader in a systematic fashion, to new methods of the stochastic optimal control theory from the very beginning. The exposition contains detailed proofs and uses new and original methods to characterize the properties of stochastic functional inclusions that, up to the present time, have only been published recently by the author. The work is divided into seven chapters, with the first two acting as an introduction, containing selected material dealing with point- and set-valued stochastic processes, and the final two devoted to applications and optimal control problems. The book presents recent and pressing issues in stochastic processes, control, differential games, optimization and their application in finance, manufacturing, queueing networks, and climate control. Written by an award-winning author in the field of stochastic differential inclusions and their application to control theory, This book is intended for students and researchers in mathematics and applications; particularly those studying optimal control theory. It is also highly relevant for students of economics and engineering. The book can also be used as a reference on stochastic differential inclusions. Knowledge of select topics in analysis and probability theory are required.

Recent Developments in Well Posed Variational Problems

Recent Developments in Well Posed Variational Problems Book
Author : Roberto Lucchetti,Julian Revalski
Publisher : Springer Science & Business Media
Release : 2013-03-09
ISBN : 9401584729
Language : En, Es, Fr & De

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Book Description :

This volume contains several surveys focused on the ideas of approximate solutions, well-posedness and stability of problems in scalar and vector optimization, game theory and calculus of variations. These concepts are of particular interest in many fields of mathematics. The idea of stability goes back at least to J. Hadamard who introduced it in the setting of differential equations; the concept of well-posedness for minimum problems is more recent (the mid-sixties) and originates with A.N. Tykhonov. It turns out that there are connections between the two properties in the sense that a well-posed problem which, at least in principle, is "easy to solve", has a solution set that does not vary too much under perturbation of the data of the problem, i.e. it is "stable". These themes have been studied in depth for minimum problems and now we have a general picture of the related phenomena in this case. But, of course, the same concepts can be studied in other more complicated situations as, e.g. vector optimization, game theory and variational inequalities. Let us mention that in several of these new areas there is not even a unique idea of what should be called approximate solution, and the latter is at the basis of the definition of well posed problem.