Nonlinear Programming Techniques For Equilibria
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Nonlinear Programming Techniques For Equilibria
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Author : Giancarlo Bigi
language : en
Publisher: Springer
Release Date : 2018-09-20
Nonlinear Programming Techniques For Equilibria written by Giancarlo Bigi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-20 with Business & Economics categories.
This book considers a range of problems in operations research, which are formulated through various mathematical models such as complementarity, variational inequalities, multiobjective optimization, fixed point problems, noncooperative games and inverse optimization. Moreover, the book subsumes all these models under a common structure that allows them to be formulated in a unique format: the Ky Fan inequality. It subsequently focuses on this unifying equilibrium format, providing a comprehensive overview of the main theoretical results and solution algorithms, together with a wealth of applications and numerical examples. Particular emphasis is placed on the role of nonlinear optimization techniques – e.g. convex optimization, nonsmooth calculus, proximal point and descent algorithms – as valuable tools for analyzing and solving Ky Fan inequalities.
Equilibrium Problems Nonsmooth Optimization And Variational Inequality Models
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Author : F. Giannessi
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-11
Equilibrium Problems Nonsmooth Optimization And Variational Inequality Models written by F. Giannessi 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 Mathematics categories.
The aim of the book is to cover the three fundamental aspects of research in equilibrium problems: the statement problem and its formulation using mainly variational methods, its theoretical solution by means of classical and new variational tools, the calculus of solutions and applications in concrete cases. The book shows how many equilibrium problems follow a general law (the so-called user equilibrium condition). Such law allows us to express the problem in terms of variational inequalities. Variational inequalities provide a powerful methodology, by which existence and calculation of the solution can be obtained.
Physical Models And Equilibrium Methods In Programming And Economics
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Author : B.S. Razumikhin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Physical Models And Equilibrium Methods In Programming And Economics written by B.S. Razumikhin 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.
It isn't that they can't see Approach your problems from the solution. the right end and begin with It is that they can't see the the answers. Then one day, problem. perhaps you will find the final qu~stion. G. K. Chesterton. The Scandal of Father Brown ITh~ Point of 'The Hermit Clad in Crane Feathers' in R. van Gulik's a Pin'. The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. HowQvQr, thQ "tree" of knowledge of mathematics and related field does not grow only by putting forth new branches. It also happ~ns, quit~ often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathe matics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.
Computing Equilibria And Fixed Points
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Author : Zaifu Yang
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Computing Equilibria And Fixed Points written by Zaifu Yang 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 2013-04-17 with Business & Economics categories.
Computing Equilibria and Fixed Points is devoted to the computation of equilibria, fixed points and stationary points. This volume is written with three goals in mind: (i) To give a comprehensive introduction to fixed point methods and to the definition and construction of Gröbner bases; (ii) To discuss several interesting applications of these methods in the fields of general equilibrium theory, game theory, mathematical programming, algebra and symbolic computation; (iii) To introduce several advanced fixed point and stationary point theorems. These methods and topics should be of interest not only to economists and game theorists concerned with the computation and existence of equilibrium outcomes in economic models and cooperative and non-cooperative games, but also to applied mathematicians, computer scientists and engineers dealing with models of highly nonlinear systems of equations (or polynomial equations).
Nonsmooth Approach To Optimization Problems With Equilibrium Constraints
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Author : Jiri Outrata
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Nonsmooth Approach To Optimization Problems With Equilibrium Constraints written by Jiri Outrata 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.
In the early fifties, applied mathematicians, engineers and economists started to pay c10se attention to the optimization problems in which another (lower-Ievel) optimization problem arises as a side constraint. One of the motivating factors was the concept of the Stackelberg solution in game theory, together with its economic applications. Other problems have been encountered in the seventies in natural sciences and engineering. Many of them are of practical importance and have been extensively studied, mainly from the theoretical point of view. Later, applications to mechanics and network design have lead to an extension of the problem formulation: Constraints in form of variation al inequalities and complementarity problems were also admitted. The term "generalized bi level programming problems" was used at first but later, probably in Harker and Pang, 1988, a different terminology was introduced: Mathematical programs with equilibrium constraints, or simply, MPECs. In this book we adhere to MPEC terminology. A large number of papers deals with MPECs but, to our knowledge, there is only one monograph (Luo et al. , 1997). This monograph concentrates on optimality conditions and numerical methods. Our book is oriented similarly, but we focus on those MPECs which can be treated by the implicit programming approach: the equilibrium constraint locally defines a certain implicit function and allows to convert the problem into a mathematical program with a nonsmooth objective.
Selected Applications Of Nonlinear Programming
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Author : Jerome Bracken
language : en
Publisher: New York : Wiley
Release Date : 1968
Selected Applications Of Nonlinear Programming written by Jerome Bracken and has been published by New York : Wiley this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Mathematics categories.
Pathways To Solutions Fixed Points And Equilibria
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Author : Willard I. Zangwill
language : en
Publisher: Prentice Hall
Release Date : 1981
Pathways To Solutions Fixed Points And Equilibria written by Willard I. Zangwill and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.
The Traffic Assignment Problem
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Author : Michael Patriksson
language : en
Publisher: Courier Dover Publications
Release Date : 2015-01-19
The Traffic Assignment Problem written by Michael Patriksson and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-19 with Mathematics categories.
This monograph provides both a unified account of the development of models and methods for the problem of estimating equilibrium traffic flows in urban areas and a survey of the scope and limitations of present traffic models. The development is described and analyzed by the use of the powerful instruments of nonlinear optimization and mathematical programming within the field of operations research. The first part is devoted to mathematical models for the analysis of transportation network equilibria; the second deals with methods for traffic equilibrium problems. This title will interest readers wishing to extend their knowledge of equilibrium modeling and analysis and of the foundations of efficient optimization methods adapted for the solution of large-scale models. In addition to its value to researchers, the treatment is suitable for advanced graduate courses in transportation, operations research, and quantitative economics.
Nonlinear Optimization
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Author : H. A. Eiselt
language : en
Publisher: Springer Nature
Release Date : 2019-11-09
Nonlinear Optimization written by H. A. Eiselt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-09 with Mathematics categories.
This book provides a comprehensive introduction to nonlinear programming, featuring a broad range of applications and solution methods in the field of continuous optimization. It begins with a summary of classical results on unconstrained optimization, followed by a wealth of applications from a diverse mix of fields, e.g. location analysis, traffic planning, and water quality management, to name but a few. In turn, the book presents a formal description of optimality conditions, followed by an in-depth discussion of the main solution techniques. Each method is formally described, and then fully solved using a numerical example.
Mathematical Programming Algorithms For Large Scale Network Equilibrium And Network Design Problems
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Author : Larry Joseph Leblanc
language : en
Publisher:
Release Date : 1973
Mathematical Programming Algorithms For Large Scale Network Equilibrium And Network Design Problems written by Larry Joseph Leblanc and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Algorithms categories.