Theory And Methods Of Vector Optimization Volume Two
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Theory And Methods Of Vector Optimization Volume Two
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Author : Yu. K. Mashunin
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2021-09-30
Theory And Methods Of Vector Optimization Volume Two written by Yu. K. Mashunin and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-30 with Mathematics categories.
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.
Theory And Methods Of Vector Optimization Volume One
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Author : Yu. K. Mashunin
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2020-03-24
Theory And Methods Of Vector Optimization Volume One written by Yu. K. Mashunin and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-24 with Mathematics categories.
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.
Theory And Methods Of Vector Optimization Volume Two
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Author : Yu. K. Mashunin
language : en
Publisher:
Release Date : 2023-04-22
Theory And Methods Of Vector Optimization Volume Two written by Yu. K. Mashunin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-22 with categories.
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.
Theory Of Vector Optimization
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Author : Dinh The Luc
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Theory Of Vector Optimization written by Dinh The Luc 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 2012-12-06 with Business & Economics categories.
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.
Vector Optimization
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Author : Johannes Jahn
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-22
Vector Optimization written by Johannes Jahn 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 2010-11-22 with Business & Economics categories.
Fundamentals and important results of vector optimization in a general setting are presented in this book. The theory developed includes scalarization, existence theorems, a generalized Lagrange multiplier rule and duality results. Applications to vector approximation, cooperative game theory and multiobjective optimization are described. The theory is extended to set optimization with particular emphasis on contingent epiderivatives, subgradients and optimality conditions. Background material of convex analysis being necessary is concisely summarized at the beginning. This second edition contains new parts on the adaptive Eichfelder-Polak method, a concrete application to magnetic resonance systems in medical engineering and additional remarks on the contribution of F.Y. Edgeworth and V. Pareto. The bibliography is updated and includes more recent important publications.
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.
Vector Optimization
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Author : Guang-ya Chen
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-07-13
Vector Optimization written by Guang-ya Chen 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 2005-07-13 with Business & Economics categories.
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.
Vector Optimization With Infimum And Supremum
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Author : Andreas Löhne
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-25
Vector Optimization With Infimum And Supremum written by Andreas Löhne 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 2011-05-25 with Business & Economics categories.
The theory of Vector Optimization is developed by a systematic usage of infimum and supremum. In order to get existence and appropriate properties of the infimum, the image space of the vector optimization problem is embedded into a larger space, which is a subset of the power set, in fact, the space of self-infimal sets. Based on this idea we establish solution concepts, existence and duality results and algorithms for the linear case. The main advantage of this approach is the high degree of analogy to corresponding results of Scalar Optimization. The concepts and results are used to explain and to improve practically relevant algorithms for linear vector optimization problems.
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.
Support Vector Machines
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Author : Naiyang Deng
language : en
Publisher: CRC Press
Release Date : 2012-12-17
Support Vector Machines written by Naiyang Deng and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-17 with Business & Economics categories.
Support Vector Machines: Optimization Based Theory, Algorithms, and Extensions presents an accessible treatment of the two main components of support vector machines (SVMs)—classification problems and regression problems. The book emphasizes the close connection between optimization theory and SVMs since optimization is one of the pillars on which SVMs are built. The authors share insight on many of their research achievements. They give a precise interpretation of statistical leaning theory for C-support vector classification. They also discuss regularized twin SVMs for binary classification problems, SVMs for solving multi-classification problems based on ordinal regression, SVMs for semi-supervised problems, and SVMs for problems with perturbations. To improve readability, concepts, methods, and results are introduced graphically and with clear explanations. For important concepts and algorithms, such as the Crammer-Singer SVM for multi-class classification problems, the text provides geometric interpretations that are not depicted in current literature. Enabling a sound understanding of SVMs, this book gives beginners as well as more experienced researchers and engineers the tools to solve real-world problems using SVMs.