Nondifferentiable And Two Level Mathematical Programming
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Nondifferentiable And Two Level Mathematical Programming
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Author : Kiyotaka Shimizu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nondifferentiable And Two Level Mathematical Programming written by Kiyotaka Shimizu 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.
The analysis and design of engineering and industrial systems has come to rely heavily on the use of optimization techniques. The theory developed over the last 40 years, coupled with an increasing number of powerful computational procedures, has made it possible to routinely solve problems arising in such diverse fields as aircraft design, material flow, curve fitting, capital expansion, and oil refining just to name a few. Mathematical programming plays a central role in each of these areas and can be considered the primary tool for systems optimization. Limits have been placed on the types of problems that can be solved, though, by the difficulty of handling functions that are not everywhere differentiable. To deal with real applications, it is often necessary to be able to optimize functions that while continuous are not differentiable in the classical sense. As the title of the book indicates, our chief concern is with (i) nondifferentiable mathematical programs, and (ii) two-level optimization problems. In the first half of the book, we study basic theory for general smooth and nonsmooth functions of many variables. After providing some background, we extend traditional (differentiable) nonlinear programming to the nondifferentiable case. The term used for the resultant problem is nondifferentiable mathematical programming. The major focus is on the derivation of optimality conditions for general nondifferentiable nonlinear programs. We introduce the concept of the generalized gradient and derive Kuhn-Tucker-type optimality conditions for the corresponding formulations.
Point To Set Maps And Mathematical Programming
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Author : P. Huard
language : en
Publisher:
Release Date : 1979
Point To Set Maps And Mathematical Programming written by P. Huard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with categories.
Differentiable stability in non convex and non differentiable programming; A multivalued approach to the farkas lemma; Extensions of the continuity of point-to-set maps: applications to fixed point algorithms; Composition und union of general algorithms of optimization; Modified lagrangians in convex programming and their generalizations; Extensions of Zangwill's theorem; On the lower semicontinuity of optimal sets in convex parametric optimization; A note on the continuity of the solution set of special dual optimization problems; Asymptotic properties of sequences iteratively generated by point-to-set maps; Generalized equations and their solutions; The fixed point approach to nonlinear programming; Convergence analysis for two-level algorithms of mathematical programming; A comparative study of several general convergence conditions for algorithms modeled by point-to-set maps.
Fuzzy And Multi Level Decision Making
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Author : E. Stanley Lee
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Fuzzy And Multi Level Decision Making written by E. Stanley Lee 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 Technology & Engineering categories.
Managerial Decisions in hierarchy organizations, such as the various manufacturing and service companies, are difficult to formalize and even more difficult to optimize. By exploring the typical fuzziness, vagueness, or the "not-well-defined" nature of such organizations, this book presents the first comprehensive treatment of this difficult and practically important problem. The advantages of the proposed fuzzy interactive approach are that it significantly reduces computational requirements. Equally, the representation of the system is made more realistic through the recognition of the inherent fuzziness of such large organizations. Both the multi-ploy and the game-like decision making processes, also known as multi-level programming and the fuzzy interactive approach, are discussed in detail. The emphasis is on numerical algorithms and numerous examples are solved and compared. The concepts of fuzzy set and fuzzy linguistic representation, which form an integral part of any managerial decision, are also discussed.
Cooperative And Noncooperative Multi Level Programming
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Author : Masatoshi Sakawa
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-18
Cooperative And Noncooperative Multi Level Programming written by Masatoshi Sakawa 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 2009-06-18 with Business & Economics categories.
To derive rational and convincible solutions to practical decision making problems in complex and hierarchical human organizations, the decision making problems are formulated as relevant mathematical programming problems which are solved by developing optimization techniques so as to exploit characteristics or structural features of the formulated problems. In particular, for resolving con?ict in decision making in hierarchical managerial or public organizations, the multi level formula tion of the mathematical programming problems has been often employed together with the solution concept of Stackelberg equilibrium. However,weconceivethatapairoftheconventionalformulationandthesolution concept is not always suf?cient to cope with a large variety of decision making situations in actual hierarchical organizations. The following issues should be taken into consideration in expression and formulation of decision making problems. Informulationofmathematicalprogrammingproblems,itistacitlysupposedthat decisions are made by a single person while game theory deals with economic be havior of multiple decision makers with fully rational judgment. Because two level mathematical programming problems are interpreted as static Stackelberg games, multi level mathematical programming is relevant to noncooperative game theory; in conventional multi level mathematical programming models employing the so lution concept of Stackelberg equilibrium, it is assumed that there is no communi cation among decision makers, or they do not make any binding agreement even if there exists such communication. However, for decision making problems in such as decentralized large ?rms with divisional independence, it is quite natural to sup pose that there exists communication and some cooperative relationship among the decision makers.
Bilevel Optimization
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Author : Stephan Dempe
language : en
Publisher: Springer Nature
Release Date : 2020-11-23
Bilevel Optimization written by Stephan Dempe and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-23 with Business & Economics categories.
2019 marked the 85th anniversary of Heinrich Freiherr von Stackelberg’s habilitation thesis “Marktform und Gleichgewicht,” which formed the roots of bilevel optimization. Research on the topic has grown tremendously since its introduction in the field of mathematical optimization. Besides the substantial advances that have been made from the perspective of game theory, many sub-fields of bilevel optimization have emerged concerning optimal control, multiobjective optimization, energy and electricity markets, management science, security and many more. Each chapter of this book covers a specific aspect of bilevel optimization that has grown significantly or holds great potential to grow, and was written by top experts in the corresponding area. In other words, unlike other works on the subject, this book consists of surveys of different topics on bilevel optimization. Hence, it can serve as a point of departure for students and researchers beginning their research journey or pursuing related projects. It also provides a unique opportunity for experienced researchers in the field to learn about the progress made so far and directions that warrant further investigation. All chapters have been peer-reviewed by experts on mathematical optimization.
Basic Mathematical Programming Theory
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Author : Giorgio Giorgi
language : en
Publisher: Springer Nature
Release Date : 2023-07-18
Basic Mathematical Programming Theory written by Giorgio Giorgi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-18 with Business & Economics categories.
The subject of (static) optimization, also called mathematical programming, is one of the most important and widespread branches of modern mathematics, serving as a cornerstone of such scientific subjects as economic analysis, operations research, management sciences, engineering, chemistry, physics, statistics, computer science, biology, and social sciences. This book presents a unified, progressive treatment of the basic mathematical tools of mathematical programming theory. The authors expose said tools, along with results concerning the most common mathematical programming problems formulated in a finite-dimensional setting, forming the basis for further study of the basic questions on the various algorithmic methods and the most important particular applications of mathematical programming problems. This book assumes no previous experience in optimization theory, and the treatment of the various topics is largely self-contained. Prerequisites are the basic tools of differential calculus for functions of several variables, the basic notions of topology and of linear algebra, and the basic mathematical notions and theoretical background used in analyzing optimization problems. The book is aimed at both undergraduate and postgraduate students interested in mathematical programming problems but also those professionals who use optimization methods and wish to learn the more theoretical aspects of these questions.
Fuzzy And Multi Level Decision Making Soft Computing Approaches
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Author : Chi-Bin Cheng
language : en
Publisher: Springer
Release Date : 2018-12-14
Fuzzy And Multi Level Decision Making Soft Computing Approaches written by Chi-Bin Cheng and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-14 with Technology & Engineering categories.
This book offers a comprehensive overview of cutting-edge approaches for decision-making in hierarchical organizations. It presents soft-computing-based techniques, including fuzzy sets, neural networks, genetic algorithms and particle swarm optimization, and shows how these approaches can be effectively used to deal with problems typical of this kind of organization. After introducing the main classical approaches applied to multiple-level programming, the book describes a set of soft-computing techniques, demonstrating their advantages in providing more efficient solutions to hierarchical decision-making problems compared to the classical methods. Based on the book Fuzzy and Multi-Level Decision Making (Springer, 2001) by Lee E.S and Shih, H., this second edition has been expanded to include the most recent findings and methods and a broader spectrum of soft computing approaches. All the algorithms are presented in detail, together with a wealth of practical examples and solutions to real-world problems, providing students, researchers and professionals with a timely, practice-oriented reference guide to the area of interactive fuzzy decision making, multi-level programming and hierarchical optimization.
Building And Solving Mathematical Programming Models In Engineering And Science
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Author : Enrique Castillo
language : en
Publisher: John Wiley & Sons
Release Date : 2011-10-24
Building And Solving Mathematical Programming Models In Engineering And Science written by Enrique Castillo 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 2011-10-24 with Mathematics categories.
Fundamental concepts of mathematical modeling Modeling is one of the most effective, commonly used tools in engineering and the applied sciences. In this book, the authors deal with mathematical programming models both linear and nonlinear and across a wide range of practical applications. Whereas other books concentrate on standard methods of analysis, the authors focus on the power of modeling methods for solving practical problems-clearly showing the connection between physical and mathematical realities-while also describing and exploring the main concepts and tools at work. This highly computational coverage includes: * Discussion and implementation of the GAMS programming system * Unique coverage of compatibility * Illustrative examples that showcase the connection between model and reality * Practical problems covering a wide range of scientific disciplines, as well as hundreds of examples and end-of-chapter exercises * Real-world applications to probability and statistics, electrical engineering, transportation systems, and more Building and Solving Mathematical Programming Models in Engineering and Science is practically suited for use as a professional reference for mathematicians, engineers, and applied or industrial scientists, while also tutorial and illustrative enough for advanced students in mathematics or engineering.
Encyclopedia Of Optimization
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Author : Christodoulos A. Floudas
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-04
Encyclopedia Of Optimization written by Christodoulos A. Floudas 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 2008-09-04 with Mathematics categories.
The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".
Intelligent Decision Technologies
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Author : Junzo Watada
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-05-20
Intelligent Decision Technologies written by Junzo Watada 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 2012-05-20 with Technology & Engineering categories.
The Intelligent Decision Technologies (IDT) International Conference encourages an interchange of research on intelligent systems and intelligent technologies that enhance or improve decision making. The focus of IDT is interdisciplinary and includes research on all aspects of intelligent decision technologies, from fundamental development to real applications. IDT has the potential to expand their support of decision making in such areas as finance, accounting, marketing, healthcare, medical and diagnostic systems, military decisions, production and operation, networks, traffic management, crisis response, human-machine interfaces, financial and stock market monitoring and prediction, and robotics. Intelligent decision systems implement advances in intelligent agents, fuzzy logic, multi-agent systems, artificial neural networks, and genetic algorithms, among others. Emerging areas of active research include virtual decision environments, social networking, 3D human-machine interfaces, cognitive interfaces, collaborative systems, intelligent web mining, e-commerce, e-learning, e-business, bioinformatics, evolvable systems, virtual humans, and designer drugs. This volume contains papers from the Fourth KES International Symposium on Intelligent Decision Technologies (KES IDT’12), hosted by researchers in Nagoya University and other institutions in Japan. This book contains chapters based on papers selected from a large number of submissions for consideration for the conference from the international community. The volume represents the current leading thought in intelligent decision technologies.