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.

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.

Multiple Criteria Optimization

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Author : Xavier Gandibleux
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11

Multiple Criteria Optimization written by Xavier Gandibleux 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 2006-04-11 with Business & Economics categories.

The generalized area of multiple criteria decision making (MCDM) can be defined as the body of methods and procedures by which the concern for multiple conflicting criteria can be formally incorporated into the analytical process. MCDM consists mostly of two branches, multiple criteria optimization and multi-criteria decision analysis (MCDA). While MCDA is typically concerned with multiple criteria problems that have a small number of alternatives often in an environment of uncertainty (location of an airport, type of drug rehabilitation program), multiple criteria optimization is typically directed at problems formulated within a mathematical programming framework, but with a stack of objectives instead of just one (river basin management, engineering component design, product distribution). It is about the most modern treatment of multiple criteria optimization that this book is concerned. I look at this book as a nicely organized and well-rounded presentation of what I view as ”new wave” topics in multiple criteria optimization. Looking back to the origins of MCDM, most people agree that it was not until about the early 1970s that multiple criteria optimization c- gealed as a field. At this time, and for about the following fifteen years, the focus was on theories of multiple objective linear programming that subsume conventional (single criterion) linear programming, algorithms for characterizing the efficient set, theoretical vector-maximum dev- opments, and interactive procedures.

Inverse And Crack Identification Problems In Engineering Mechanics

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Author : Georgios E. Stavroulakis
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21

Inverse And Crack Identification Problems In Engineering Mechanics written by Georgios E. Stavroulakis 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 2013-11-21 with Mathematics categories.

Inverse and crack identification problems are of paramount importance for health monitoring and quality control purposes arising in critical applications in civil, aeronautical, nuclear, and general mechanical engineering. Mathematical modeling and the numerical study of these problems require high competence in computational mechanics and applied optimization. This is the first monograph which provides the reader with all the necessary information. Delicate computational mechanics modeling, including nonsmooth unilateral contact effects, is done using boundary element techniques, which have a certain advantage for the construction of parametrized mechanical models. Both elastostatic and harmonic or transient dynamic problems are considered. The inverse problems are formulated as output error minimization problems and they are theoretically studied as a bilevel optimization problem, also known as a mathematical problem with equilibrium constraints. Beyond classical numerical optimization, soft computing tools (neural networks and genetic algorithms) and filter algorithms are used for the numerical solution. The book provides all the required material for the mathematical and numerical modeling of crack identification testing procedures in statics and dynamics and includes several thoroughly discussed applications, for example, the impact-echo nondestructive evaluation technique. Audience: The book will be of interest to structural and mechanical engineers involved in nondestructive testing and quality control projects as well as to research engineers and applied mathematicians who study and solve related inverse problems. People working on applied optimization and soft computing will find interesting problems to apply to their methods and all necessary material to continue research in this field.

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.

Nonlinear Optimization And Related Topics

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Author : Gianni Pillo
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Nonlinear Optimization And Related Topics written by Gianni Pillo 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 2013-06-29 with Mathematics categories.

This volume contains the edited texts of the lectures presented at the Workshop on Nonlinear Optimization held in Erice, Sicily, at the "G. Stampacchia" School of Mathematics of the "E. Majorana" Centre for Scientific Culture, June 23 -July 2, 1998. In the tradition of these meetings, the main purpose was to review and discuss recent advances and promising research trends concerning theory, algorithms and innovative applications in the field of Nonlinear Optimization, and of related topics such as Convex Optimization, Nonsmooth Optimization, Variational Inequalities and Complementarity Problems. The meeting was attended by 83 people from 21 countries. Besides the lectures, several formal and informal discussions took place. The result was a wide and deep knowledge of the present research tendencies in the field. We wish to express our appreciation for the active contribution of all the par ticipants in the meeting. Our gratitude is due to the Ettore Majorana Centre in Erice, which offered its facilities and rewarding environment: its staff was certainly instrumental for the success of the meeting. Our gratitude is also due to Francisco Facchinei and Massimo Roma for the effort and time devoted as members of the Organising Committee. We are indebted to the Italian National Research Council, and in particular to the Group on Functional Analysis and its Applications and to the Committees on Engineering Sciences and on Information Sciences and Technolo gies for their financial support. Finally, we address our thanks to Kluwer Academic Publishers for having offered to publish this volume.

Graph Theory And Combinatorial Optimization

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Author : David Avis
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-04-28

Graph Theory And Combinatorial Optimization written by David Avis 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 2005-04-28 with Business & Economics categories.

Graph theory is very much tied to the geometric properties of optimization and combinatorial optimization. Moreover, graph theory's geometric properties are at the core of many research interests in operations research and applied mathematics. Its techniques have been used in solving many classical problems including maximum flow problems, independent set problems, and the traveling salesman problem. Graph Theory and Combinatorial Optimization explores the field's classical foundations and its developing theories, ideas and applications to new problems. The book examines the geometric properties of graph theory and its widening uses in combinatorial optimization theory and application. The field's leading researchers have contributed chapters in their areas of expertise.

Pseudolinear Functions And Optimization

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Author : Shashi Kant Mishra
language : en
Publisher: CRC Press
Release Date : 2014-12-18

Pseudolinear Functions And Optimization written by Shashi Kant Mishra and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-18 with Business & Economics categories.

Pseudolinear Functions and Optimization is the first book to focus exclusively on pseudolinear functions, a class of generalized convex functions. It discusses the properties, characterizations, and applications of pseudolinear functions in nonlinear optimization problems.The book describes the characterizations of solution sets of various optimiza

Noniterative Coordination In Multilevel Systems

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Author : Todor Stoilov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Noniterative Coordination In Multilevel Systems written by Todor Stoilov 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 Mathematics categories.

Multilevel decision theory arises to resolve the contradiction between increasing requirements towards the process of design, synthesis, control and management of complex systems and the limitation of the power of technical, control, computer and other executive devices, which have to perform actions and to satisfy requirements in real time. This theory rises suggestions how to replace the centralised management of the system by hierarchical co-ordination of sub-processes. All sub-processes have lower dimensions, which support easier management and decision making. But the sub-processes are interconnected and they influence each other. Multilevel systems theory supports two main methodological tools: decomposition and co-ordination. Both have been developed, and implemented in practical applications concerning design, control and management of complex systems. In general, it is always beneficial to find the best or optimal solution in processes of system design, control and management. The real tendency towards the best (optimal) decision requires to present all activities in the form of a definition and then the solution of an appropriate optimization problem. Every optimization process needs the mathematical definition and solution of a well stated optimization problem. These problems belong to two classes: static optimization and dynamic optimization. Static optimization problems are solved applying methods of mathematical programming: conditional and unconditional optimization. Dynamic optimization problems are solved by methods of variation calculus: Euler Lagrange method; maximum principle; dynamical programming.

Financial Transmission Rights

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Author : Juan Rosellón
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-15

Financial Transmission Rights written by Juan Rosellón 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 2013-03-15 with Business & Economics categories.

Whilst financial rights have appeared as a successful ingredient in North-American power markets, they have their shortcomings both theoretically and in practice. Financial Transmission Rights: Analysis, Experiences and Prospects present a systematic and comprehensive overview of financial transmission rights (FTRS). Following a general introduction to FTRs, including chapters to explain transmission pricing and the general properties of FTRS, experts in the field provide discussions on wide scope of topics. These include: Varying perspectives on FTRS: from electrical engineers to economists, Different mathematical formulations of FTRS Financial Hedging using FTRS, and Alternative solutions to FTRs The detail, expertise and range of content makes Financial Transmission Rights: Analysis, Experiences and Prospect an essential resource for electricity market specialists both at academic and professional levels. “This is THE BOOK we were all expecting to address all key ‘Financial Transmission Rights’ issues. It is comprehensive and reader friendly. You can pick at will in its menu: more or less theory, a bit of maths or none, empirical review of real cases or numerical simulations of many feasible options. Big names rally there to delight you like: Hogan , Oren, Perez-Arriaga, Smeers, Hobbs and... Rosellón. More than a must read: a light house, a map and a survival kit.” Jean – Michel Glachant, Director Florence School, Holder Loyola de Palacio Chair, Chief-editor Economics of Energy & Environmental Policy. "In the last two decades, economists have developed a better understanding of the impact of financial rights on risk management, market power and network expansion in electricity markets, while power systems have experimented with such rights. Striking a good balance between academics and practitioners, always at the frontier of the field, written by the best experts, this volume is essential reading for all those- power systems’ managers and users, regulators, students and researchers- who want to understand the new electricity environment and predict its evolution." Jean Tirole, Toulouse School of Economics and Institute for Industrial Economics (IDEI) Further comments inside.