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Author : Casti
Publisher : Academic Press
ISBN 13 : 0080956564
Total Pages : 231 pages
Book Rating : 4.0/5 (89 download)
Download or read book Vector-Valued Optimization Problems in Control Theory written by Casti and published by Academic Press. This book was released on 1980-06-19 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vector-Valued Optimization Problems in Control Theory
Author : N. U. Ahmed
Publisher : Springer Nature
ISBN 13 : 3030821390
Total Pages : 328 pages
Book Rating : 4.0/5 (38 download)
Download or read book Optimal Control of Dynamic Systems Driven by Vector Measures written by N. U. Ahmed and published by Springer Nature. This book was released on 2021-09-13 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the development of optimal control theory for finite dimensional systems governed by deterministic and stochastic differential equations driven by vector measures. The book deals with a broad class of controls, including regular controls (vector-valued measurable functions), relaxed controls (measure-valued functions) and controls determined by vector measures, where both fully and partially observed control problems are considered. In the past few decades, there have been remarkable advances in the field of systems and control theory thanks to the unprecedented interaction between mathematics and the physical and engineering sciences. Recently, optimal control theory for dynamic systems driven by vector measures has attracted increasing interest. This book presents this theory for dynamic systems governed by both ordinary and stochastic differential equations, including extensive results on the existence of optimal controls and necessary conditions for optimality. Computational algorithms are developed based on the optimality conditions, with numerical results presented to demonstrate the applicability of the theoretical results developed in the book. This book will be of interest to researchers in optimal control or applied functional analysis interested in applications of vector measures to control theory, stochastic systems driven by vector measures, and related topics. In particular, this self-contained account can be a starting point for further advances in the theory and applications of dynamic systems driven and controlled by vector measures.
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Author : Mindija Evgen'evič Salukvadze
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (163 download)
Download or read book Vector-valued optimization problems in control theory (Zadači vektornaj optimizacii v teorii upravlenija, engl.) [Von] M.E. Salukvadze written by Mindija Evgen'evič Salukvadze and published by . This book was released on 1979 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J Gregory
Publisher : CRC Press
ISBN 13 : 1351087762
Total Pages : 218 pages
Book Rating : 4.3/5 (51 download)
Download or read book Constrained Optimization In The Calculus Of Variations and Optimal Control Theory written by J Gregory and published by CRC Press. This book was released on 2018-01-18 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The major purpose of this book is to present the theoretical ideas and the analytical and numerical methods to enable the reader to understand and efficiently solve these important optimizational problems.The first half of this book should serve as the major component of a classical one or two semester course in the calculus of variations and optimal control theory. The second half of the book will describe the current research of the authors which is directed to solving these problems numerically. In particular, we present new reformulations of constrained problems which leads to unconstrained problems in the calculus of variations and new general, accurate and efficient numerical methods to solve the reformulated problems. We believe that these new methods will allow the reader to solve important problems.
Author : Slukvadze
Publisher : Academic Press
ISBN 13 : 0080958788
Total Pages : 425 pages
Book Rating : 4.0/5 (89 download)
Download or read book The Vector-Valued Maximin written by Slukvadze and published by Academic Press. This book was released on 1993-12-09 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Vector-Valued Maximin
Author : Johannes Jahn
Publisher : Springer Science & Business Media
ISBN 13 : 3540248285
Total Pages : 471 pages
Book Rating : 4.5/5 (42 download)
Download or read book Vector Optimization written by Johannes Jahn and published by Springer Science & Business Media. This book was released on 2013-06-05 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: In vector optimization one investigates optimal elements such as min imal, strongly minimal, properly minimal or weakly minimal elements of a nonempty subset of a partially ordered linear space. The prob lem of determining at least one of these optimal elements, if they exist at all, is also called a vector optimization problem. Problems of this type can be found not only in mathematics but also in engineer ing and economics. Vector optimization problems arise, for exam ple, in functional analysis (the Hahn-Banach theorem, the lemma of Bishop-Phelps, Ekeland's variational principle), multiobjective pro gramming, multi-criteria decision making, statistics (Bayes solutions, theory of tests, minimal covariance matrices), approximation theory (location theory, simultaneous approximation, solution of boundary value problems) and cooperative game theory (cooperative n player differential games and, as a special case, optimal control problems). In the last decade vector optimization has been extended to problems with set-valued maps. This new field of research, called set optimiza tion, seems to have important applications to variational inequalities and optimization problems with multivalued data. The roots of vector optimization go back to F. Y. Edgeworth (1881) and V. Pareto (1896) who has already given the definition of the standard optimality concept in multiobjective optimization. But in mathematics this branch of optimization has started with the leg endary paper of H. W. Kuhn and A. W. Tucker (1951). Since about v Vl Preface the end of the 60's research is intensively made in vector optimization.
Author : Aram Arutyunov
Publisher : Springer
ISBN 13 : 3030022609
Total Pages : 197 pages
Book Rating : 4.0/5 (3 download)
Download or read book Optimal Impulsive Control written by Aram Arutyunov and published by Springer. This book was released on 2018-12-17 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal Impulsive Control explores the class of impulsive dynamic optimization problems—problems that stem from the fact that many conventional optimal control problems do not have a solution in the classical setting—which is highly relevant with regard to engineering applications. The absence of a classical solution naturally invokes the so-called extension, or relaxation, of a problem, and leads to the notion of generalized solution which encompasses the notions of generalized control and trajectory; in this book several extensions of optimal control problems are considered within the framework of optimal impulsive control theory. In this framework, the feasible arcs are permitted to have jumps, while the conventional absolutely continuous trajectories may fail to exist. The authors draw together various types of their own results, centered on the necessary conditions of optimality in the form of Pontryagin’s maximum principle and the existence theorems, which shape a substantial body of optimal impulsive control theory. At the same time, they present optimal impulsive control theory in a unified framework, introducing the different paradigmatic problems in increasing order of complexity. The rationale underlying the book involves addressing extensions increasing in complexity from the simplest case provided by linear control systems and ending with the most general case of a totally nonlinear differential control system with state constraints. The mathematical models presented in Optimal Impulsive Control being encountered in various engineering applications, this book will be of interest to both academic researchers and practising engineers.
Author : Akhtar A. Khan
Publisher : CRC Press
ISBN 13 : 1351712063
Total Pages : 226 pages
Book Rating : 4.3/5 (517 download)
Download or read book Variational Analysis and Set Optimization written by Akhtar A. Khan and published by CRC Press. This book was released on 2019-06-07 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the latest advances in variational analysis and set / vector optimization, including uncertain optimization, optimal control and bilevel optimization. Recent developments concerning scalarization techniques, necessary and sufficient optimality conditions and duality statements are given. New numerical methods for efficiently solving set optimization problems are provided. Moreover, applications in economics, finance and risk theory are discussed. Summary The objective of this book is to present advances in different areas of variational analysis and set optimization, especially uncertain optimization, optimal control and bilevel optimization. Uncertain optimization problems will be approached from both a stochastic as well as a robust point of view. This leads to different interpretations of the solutions, which widens the choices for a decision-maker given his preferences. Recent developments regarding linear and nonlinear scalarization techniques with solid and nonsolid ordering cones for solving set optimization problems are discussed in this book. These results are useful for deriving optimality conditions for set and vector optimization problems. Consequently, necessary and sufficient optimality conditions are presented within this book, both in terms of scalarization as well as generalized derivatives. Moreover, an overview of existing duality statements and new duality assertions is given. The book also addresses the field of variable domination structures in vector and set optimization. Including variable ordering cones is especially important in applications such as medical image registration with uncertainties. This book covers a wide range of applications of set optimization. These range from finance, investment, insurance, control theory, economics to risk theory. As uncertain multi-objective optimization, especially robust approaches, lead to set optimization, one main focus of this book is uncertain optimization. Important recent developments concerning numerical methods for solving set optimization problems sufficiently fast are main features of this book. These are illustrated by various examples as well as easy-to-follow-steps in order to facilitate the decision process for users. Simple techniques aimed at practitioners working in the fields of mathematical programming, finance and portfolio selection are presented. These will help in the decision-making process, as well as give an overview of nondominated solutions to choose from.
Author : Qamrul Hasan Ansari
Publisher : Springer
ISBN 13 : 3319630490
Total Pages : 517 pages
Book Rating : 4.3/5 (196 download)
Download or read book Vector Variational Inequalities and Vector Optimization written by Qamrul Hasan Ansari and published by Springer. This book was released on 2017-10-31 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems. It is the first-ever book to introduce well-posedness and sensitivity analysis for vector equilibrium problems. The first chapter provides basic notations and results from the areas of convex analysis, functional analysis, set-valued analysis and fixed-point theory for set-valued maps, as well as a brief introduction to variational inequalities and equilibrium problems. Chapter 2 presents an overview of analysis over cones, including continuity and convexity of vector-valued functions. The book then shifts its focus to solution concepts and classical methods in vector optimization. It describes the formulation of vector variational inequalities and their applications to vector optimization, followed by separate chapters on linear scalarization, nonsmooth and generalized vector variational inequalities. Lastly, the book introduces readers to vector equilibrium problems and generalized vector equilibrium problems. Written in an illustrative and reader-friendly way, the book offers a valuable resource for all researchers whose work involves optimization and vector optimization.
Author : Elliot R. Lieberman
Publisher : Academic Press
ISBN 13 : 1483265501
Total Pages : 398 pages
Book Rating : 4.4/5 (832 download)
Download or read book Multi-Objective Programming in the USSR written by Elliot R. Lieberman and published by Academic Press. This book was released on 2014-05-12 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical Modeling and Decision Science: Multi-Objective Programming in the USSR provides information pertinent to multi-objective programming that has emerged as an increasingly active area of research in the fields of applied mathematics, operations research, and decision and management science. This book traces and analyzes the development of Soviet multi-objective programming. Organized into 24 chapters, this book begins with an overview of the research institutes most actively involved in multi-objective programming research. This text then presents an analytical framework for grouping and classifying the diverse Soviet methods. Other chapters consider the methods and then evaluated according to the significance and soundness of its basic approach and its kinship to other methods. This book discusses as well some significant Soviet theoretical research and several distinctive approaches proposed by Soviet researchers for comparing the effectiveness of alternative interactive multi-objective programming method. The final chapter deals with distinctive Soviet tendencies in multi-objective research. This book is a valuable resource for economists.
Author : Vladislav I. Zhukovskiy
Publisher : CRC Press
ISBN 13 : 1000370755
Total Pages : 325 pages
Book Rating : 4.0/5 (3 download)
Download or read book The Golden Rule of Ethics written by Vladislav I. Zhukovskiy and published by CRC Press. This book was released on 2021-04-15 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book synthesizes the game-theoretic modeling of decision-making processes and an ancient moral requirement called the Golden Rule of ethics (GR). This rule states "Behave to others as you would like them to behave to you." The GR is one of the oldest, most widespread, and specific moral requirements that appear in Christianity, Islam, Judaism, Buddhism, and Confucianism. This book constructs and justifies mathematical models of dynamic socio-economic processes and phenomena that reveal the mechanism of the GR and are based on the concept of Berge equilibrium. The GR can be naturally used for resolving or balancing conflicts, and its "altruistic character" obviously excludes wars, blood-letting, and armed clashes. The previous book by the authors, The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics, covers the static case of the GR. In this book, the dynamic case of the GR is investigated using the altruistic concept of Berge equilibrium and three factors as follows: 1) a modification of N.N. Krasovskii’s mathematical formalization of differential positional games (DPGs), in view of the counterexamples given by A.I. Subbotin and A.F. Kononenko; 2) the method of guiding control, proposed by N.N. Krasovskii; and 3) the Germier convolution of the payoff functions of different players. Additionally, this book features exercises, problems, and solution tips collected together in Appendix 1, as well as new approaches to conflict resolution as presented in Appendices 2 to 4. This book will be of use to undergraduate and graduate students and experts in the field of decision-making in complex control and management systems, as well as anyone interested in game theory and applications.
Author :
Publisher :
ISBN 13 :
Total Pages : 952 pages
Book Rating : 4.:/5 (31 download)
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1975 with total page 952 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Donald E. Kirk
Publisher : Courier Corporation
ISBN 13 : 0486135071
Total Pages : 466 pages
Book Rating : 4.4/5 (861 download)
Download or read book Optimal Control Theory written by Donald E. Kirk and published by Courier Corporation. This book was released on 2012-04-26 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Upper-level undergraduate text introduces aspects of optimal control theory: dynamic programming, Pontryagin's minimum principle, and numerical techniques for trajectory optimization. Numerous figures, tables. Solution guide available upon request. 1970 edition.
Author : Mindia E. Salukvadze
Publisher : Springer Nature
ISBN 13 : 3030255468
Total Pages : 290 pages
Book Rating : 4.0/5 (32 download)
Download or read book The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics written by Mindia E. Salukvadze and published by Springer Nature. This book was released on 2020-02-18 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to elaborate on the main principles of the theory of the Berge equilibrium by answering the following two questions: What are the basic properties of the Berge equilibrium? Does the Berge equilibrium exist, and how can it be calculated? The Golden Rule of ethics, which appears in Christianity, Judaism, Islam, Buddhism, Confucianism and other world religions, states the following: “Behave towards others as you would like them to behave towards you." In any game, each party of conflict seeks to maximize some payoff. Therefore, for each player, the Golden Rule is implemented through the maximization of his/her payoff by all other players, which matches well with the concept of the Berge equilibrium. The approach presented here will be of particular interest to researchers (including undergraduates and graduates) and economists focused on decision-making under complex conflict conditions. The peaceful resolution of conflicts is the cornerstone of the approach: as a matter of fact, the Golden Rule precludes military clashes and violence. In turn, the new approach requires new methods; in particular, the existence problems are reduced to saddle point design for the Germeier convolution of payoff functions, with further transition to mixed strategies in accordance with the standard procedure employed by E. Borel, J. von Neumann, J. Nash, and their followers. Moreover, this new approach has proven to be efficient and fruitful with regard to a range of other important problems in mathematical game theory, which are considered in the Appendix.
Author : Altannar Chinchuluun
Publisher : Springer Science & Business Media
ISBN 13 : 0387894950
Total Pages : 508 pages
Book Rating : 4.3/5 (878 download)
Download or read book Optimization and Optimal Control written by Altannar Chinchuluun and published by Springer Science & Business Media. This book was released on 2010-07-07 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization and optimal control are the main tools in decision making. Because of their numerous applications in various disciplines, research in these areas is accelerating at a rapid pace. “Optimization and Optimal Control: Theory and Applications” brings together the latest developments in these areas of research as well as presents applications of these results to a wide range of real-world problems. This volume can serve as a useful resource for researchers, practitioners, and advanced graduate students of mathematics and engineering working in research areas where results in optimization and optimal control can be applied.
Author : Suresh P. Sethi
Publisher : Springer
ISBN 13 : 3319982370
Total Pages : 577 pages
Book Rating : 4.3/5 (199 download)
Download or read book Optimal Control Theory written by Suresh P. Sethi and published by Springer. This book was released on 2018-11-28 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fully revised 3rd edition offers an introduction to optimal control theory and its diverse applications in management science and economics. It brings to students the concept of the maximum principle in continuous, as well as discrete, time by using dynamic programming and Kuhn-Tucker theory. While some mathematical background is needed, the emphasis of the book is not on mathematical rigor, but on modeling realistic situations faced in business and economics. The book exploits optimal control theory to the functional areas of management including finance, production and marketing and to economics of growth and of natural resources. In addition, this new edition features materials on stochastic Nash and Stackelberg differential games and an adverse selection model in the principal-agent framework. The book provides exercises for each chapter and answers to selected exercises to help deepen the understanding of the material presented. Also included are appendices comprised of supplementary material on the solution of differential equations, the calculus of variations and its relationships to the maximum principle, and special topics including the Kalman filter, certainty equivalence, singular control, a global saddle point theorem, Sethi-Skiba points, and distributed parameter systems. Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as a foundation for the book, which the author has applied to business management problems developed from his research and classroom instruction. The new edition has been completely refined and brought up to date. Ultimately this should continue to be a valuable resource for graduate courses on applied optimal control theory, but also for financial and industrial engineers, economists, and operational researchers concerned with the application of dynamic optimization in their fields.
Author :
Publisher :
ISBN 13 :
Total Pages : 604 pages
Book Rating : 4.E/5 ( download)
Download or read book Problems of control and information theory written by and published by . This book was released on 1977 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt:
