Theory and Methods of Vector Optimization (Volume Two) PDF Download
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Author: Yu. K. Mashunin
Publisher: Cambridge Scholars Publishing
ISBN: 1527575489
Category : Mathematics
Languages : en
Pages : 290
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Book Description
This second volume presents research in the field of the mathematical model operation of economic systems, again using as a basis the theory and methods of vector optimization. This volume includes three chapters. The first chapter deals with issues related to the theory of the company, modeling and decision-making, while the second deals with issues related to modeling and decision-making in market systems. The third chapter deals with issues related to modeling, forecasting and decision-making.
Author: Yu. K. Mashunin
Publisher: Cambridge Scholars Publishing
ISBN: 1527575489
Category : Mathematics
Languages : en
Pages : 290
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Book Description
This second volume presents research in the field of the mathematical model operation of economic systems, again using as a basis the theory and methods of vector optimization. This volume includes three chapters. The first chapter deals with issues related to the theory of the company, modeling and decision-making, while the second deals with issues related to modeling and decision-making in market systems. The third chapter deals with issues related to modeling, forecasting and decision-making.
Author: Yu. K. Mashunin
Publisher: Cambridge Scholars Publishing
ISBN: 1527548775
Category : Mathematics
Languages : en
Pages : 195
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Book Description
This first volume presents the theory and methods of solving vector optimization problems, using initial definitions that include axioms and the optimality principle. This book proves, mathematically, that the result it presents for the solution of the vector (multi-criteria) problem is the optimal outcome, and, as such, solves the problem of vector optimization for the first time. It shows that applied methods of solving vector optimization problems can be used by researchers in modeling and simulating the development of economic systems and technical (engineering) systems.
Author: Dinh The Luc
Publisher: Springer Science & Business Media
ISBN: 3642502806
Category : Business & Economics
Languages : en
Pages : 183
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Book Description
These notes grew out of a series of lectures given by the author at the Univer sity of Budapest during 1985-1986. Additional results have been included which were obtained while the author was at the University of Erlangen-Niirnberg under a grant of the Alexander von Humboldt Foundation. Vector optimization has two main sources coming from economic equilibrium and welfare theories of Edgeworth (1881) and Pareto (1906) and from mathemat ical backgrounds of ordered spaces of Cantor (1897) and Hausdorff (1906). Later, game theory of Borel (1921) and von Neumann (1926) and production theory of Koopmans (1951) have also contributed to this area. However, only in the fifties, after the publication of Kuhn-Tucker's paper (1951) on the necessary and sufficient conditions for efficiency, and of Deubreu's paper (1954) on valuation equilibrium and Pareto optimum, has vector optimization been recognized as a mathematical discipline. The stretching development of this field began later in the seventies and eighties. Today there are a number of books on vector optimization. Most of them are concerned with the methodology and the applications. Few of them offer a systematic study of the theoretical aspects. The aim of these notes is to pro vide a unified background of vector optimization,with the emphasis on nonconvex problems in infinite dimensional spaces ordered by convex cones. The notes are arranged into six chapters. The first chapter presents prelim inary material.
Author: David G. Luenberger
Publisher: John Wiley & Sons
ISBN: 9780471181170
Category : Technology & Engineering
Languages : en
Pages : 348
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Book Description
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.
Author: Johannes Jahn
Publisher: Springer Science & Business Media
ISBN: 3540248285
Category : Business & Economics
Languages : en
Pages : 471
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Book Description
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: Guang-ya Chen
Publisher: Springer Science & Business Media
ISBN: 9783540212898
Category : Business & Economics
Languages : en
Pages : 324
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Book Description
This book is devoted to vector or multiple criteria approaches in optimization. Topics covered include: vector optimization, vector variational inequalities, vector variational principles, vector minmax inequalities and vector equilibrium problems. In particular, problems with variable ordering relations and set-valued mappings are treated. The nonlinear scalarization method is extensively used throughout the book to deal with various vector-related problems. The results presented are original and should be interesting to researchers and graduates in applied mathematics and operations research. Readers will benefit from new methods and ideas for handling multiple criteria decision problems.
Author: Alexander Statnikov
Publisher: World Scientific
ISBN: 9814324388
Category : Computers
Languages : en
Pages : 200
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Book Description
Support Vector Machines (SVMs) are among the most important recent developments in pattern recognition and statistical machine learning. They have found a great range of applications in various fields including biology and medicine. However, biomedical researchers often experience difficulties grasping both the theory and applications of these important methods because of lack of technical background. The purpose of this book is to introduce SVMs and their extensions and allow biomedical researchers to understand and apply them in real-life research in a very easy manner. The book is to consist of two volumes: theory and methods (Volume 1) and cases studies (Volume 2).The proposed book follows the approach of ?programmed learning? whereby material is presented in short sections called ?frames?. Each frame consists of a very small amount of information to be learned, a multiple choice quiz, and answers to the quiz. The reader can proceed to the next frame only after verifying the correct answers to the current frame.
Author: Yoshikazu Sawaragi
Publisher: Springer Science & Business Media
ISBN: 3642466079
Category : Business & Economics
Languages : en
Pages : 462
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Book Description
These proceedings include papers presented at the VII-th Internatio nal Conference on Multiple Criteria Decision Making which was held in Kyoto/Japan on August 18-22, 1986. Multiple Criteria Decision Making (MCDM) has been a greatly import ant subject in many practical fields, for example, in planning, design, control and management in both private and public sectors. After remark able developments of theory, methodology and pilot case studies in rec ent years, it is now facing the stage of real applications and develop ment of more sophisticated methodology as interactive intelligent decision support systems. The conference aimed to provide a significant contribu tion to the future of MCDM as one of total systems including human factors: Substantial emphasis was given to knowledge engineering and cognitive sci ence. The conference inherits the tradition and the style of the previous conferences: (1) Jouy-en-Josas/France (1975), (2) Buffalo/U.S.A. (1977), (3) Konigswinter/FRG (1978), (4) Delaware/U.S.A. (1980), (5) Mons/Belgium (1982), (6) Cleveland/U.S.A. (1984). This time a great many Japanese com panies provided grants for the conference. As a result, the total number of participants was over 120, and a computer demonstration could be reali zed on an extensive scale as well as the conference sessions. Throughout the conference, it was observed that MCDM is making steady progress not only in theory but also as a tool for decision support.
Author: Mikhail J. Atallah
Publisher: CRC Press
ISBN: 1584888237
Category : Computers
Languages : en
Pages : 974
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Book Description
Algorithms and Theory of Computation Handbook, Second Edition: General Concepts and Techniques provides an up-to-date compendium of fundamental computer science topics and techniques. It also illustrates how the topics and techniques come together to deliver efficient solutions to important practical problems. Along with updating and revising many
Author: Nicolas Hadjisavvas
Publisher: Springer Science & Business Media
ISBN: 3642566456
Category : Mathematics
Languages : en
Pages : 422
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Book Description
Various generalizations of convex functions have been introduced in areas such as mathematical programming, economics, management science, engineering, stochastics and applied sciences, for example. Such functions preserve one or more properties of convex functions and give rise to models which are more adaptable to real-world situations than convex models. Similarly, generalizations of monotone maps have been studied recently. A growing literature of this interdisciplinary field has appeared, and a large number of international meetings are entirely devoted or include clusters on generalized convexity and generalized monotonicity. The present book contains a selection of refereed papers presented at the 6th International Symposium on Generalized Convexity/Monotonicity, and aims to review the latest developments in the field.
