Nonlinear Programming Techniques For Equilibria

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Nonlinear Programming Techniques for Equilibria

Author : Giancarlo Bigi
Publisher : Springer
ISBN 13 : 3030002055
Total Pages : 127 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Nonlinear Programming Techniques for Equilibria by : Giancarlo Bigi

Download or read book Nonlinear Programming Techniques for Equilibria written by Giancarlo Bigi and published by Springer. This book was released on 2018-09-20 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonlinear Programming Techniques for Equilibria

Author : Giancarlo Bigi
Publisher : Springer
ISBN 13 : 9783030130923
Total Pages : 120 pages
Book Rating : 4.1/5 (39 download)

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Book Synopsis Nonlinear Programming Techniques for Equilibria by : Giancarlo Bigi

Download or read book Nonlinear Programming Techniques for Equilibria written by Giancarlo Bigi and published by Springer. This book was released on 2019-12-10 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : F. Giannessi
Publisher : Springer Science & Business Media
ISBN 13 : 0306480263
Total Pages : 304 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models by : F. Giannessi

Download or read book Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models written by F. Giannessi and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonlinear Programming

Author : Anthony V. Fiacco
Publisher : SIAM
ISBN 13 : 9781611971316
Total Pages : 226 pages
Book Rating : 4.9/5 (713 download)

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Book Synopsis Nonlinear Programming by : Anthony V. Fiacco

Download or read book Nonlinear Programming written by Anthony V. Fiacco and published by SIAM. This book was released on 1990-01-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent interest in interior point methods generated by Karmarkar's Projective Scaling Algorithm has created a new demand for this book because the methods that have followed from Karmarkar's bear a close resemblance to those described. There is no other source for the theoretical background of the logarithmic barrier function and other classical penalty functions. Analyzes in detail the "central" or "dual" trajectory used by modern path following and primal/dual methods for convex and general linear programming. As researchers begin to extend these methods to convex and general nonlinear programming problems, this book will become indispensable to them.

Selected Applications of Nonlinear Programming

Author : Jerome Bracken
Publisher : New York : Wiley
ISBN 13 :
Total Pages : 136 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Selected Applications of Nonlinear Programming by : Jerome Bracken

Download or read book Selected Applications of Nonlinear Programming written by Jerome Bracken and published by New York : Wiley. This book was released on 1968 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Refinements of the Nash Equilibrium Concept

Author : E. van Damme
Publisher : Springer Science & Business Media
ISBN 13 : 3642499708
Total Pages : 161 pages
Book Rating : 4.6/5 (424 download)

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Book Synopsis Refinements of the Nash Equilibrium Concept by : E. van Damme

Download or read book Refinements of the Nash Equilibrium Concept written by E. van Damme and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, noncooperative games are studied. Since in a noncooperative game binding agreements are not possible, the solution of such a game has to be self enforcing, i. e. a Nash equilibrium (NASH [1950,1951J). In general, however, a game may possess many equilibria and so the problem arises which one of these should be chosen as the solution. It was first pointed out explicitly in SELTEN [1965J that I not all Nash equilibria of an extensive form game are qualified to be selected as the solution, since an equilibrium may prescribe irrational behavior at unreached parts of the game tree. Moreover, also for normal form games not all Nash equilibria are eligible, since an equilibrium need not be robust with respect to slight perturba tions in the data of the game. These observations lead to the conclusion that the Nash equilibrium concept has to be refined in order to obtain sensible solutions for every game. In the monograph, various refinements of the Nash equilibrium concept are studied. Some of these have been proposed in the literature, but others are presented here for the first time. The objective is to study the relations between these refine ments;to derive characterizations and to discuss the underlying assumptions. The greater part of the monograph (the chapters 2-5) is devoted to the study of normal form games. Extensive form games are considered in chapter 6.

Game Theory

Author : E. N. Barron
Publisher : John Wiley & Sons
ISBN 13 : 1118216938
Total Pages : 574 pages
Book Rating : 4.1/5 (182 download)

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Book Synopsis Game Theory by : E. N. Barron

Download or read book Game Theory written by E. N. Barron and published by John Wiley & Sons. This book was released on 2013-04-22 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exciting new edition of the popular introduction to game theory and its applications The thoroughly expanded Second Edition presents a unique, hands-on approach to game theory. While most books on the subject are too abstract or too basic for mathematicians, Game Theory: An Introduction, Second Edition offers a blend of theory and applications, allowing readers to use theory and software to create and analyze real-world decision-making models. With a rigorous, yet accessible, treatment of mathematics, the book focuses on results that can be used to determine optimal game strategies. Game Theory: An Introduction, Second Edition demonstrates how to use modern software, such as MapleTM, Mathematica®, and Gambit, to create, analyze, and implement effective decision-making models. Coverage includes the main aspects of game theory including the fundamentals of two-person zero-sum games, cooperative games, and population games as well as a large number of examples from various fields, such as economics, transportation, warfare, asset distribution, political science, and biology. The Second Edition features: • A new chapter on extensive games, which greatly expands the implementation of available models • New sections on correlated equilibria and exact formulas for three-player cooperative games • Many updated topics including threats in bargaining games and evolutionary stable strategies • Solutions and methods used to solve all odd-numbered problems • A companion website containing the related Maple and Mathematica data sets and code A trusted and proven guide for students of mathematics and economics, Game Theory: An Introduction, Second Edition is also an excellent resource for researchers and practitioners in economics, finance, engineering, operations research, statistics, and computer science.

Traffic Equilibrium Methods

Author : M.A. Florian
Publisher : Springer Science & Business Media
ISBN 13 : 364248123X
Total Pages : 457 pages
Book Rating : 4.6/5 (424 download)

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Book Synopsis Traffic Equilibrium Methods by : M.A. Florian

Download or read book Traffic Equilibrium Methods written by M.A. Florian and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interest in the mathematical modeling of transportation systems stems from the need to predict how people might make use of new or improved transport infrastruc ture in order to evaluate the benefit of the required investments. To this end it is necessary to build models of the demand for transportation and models that de termine the way in which people who travel use the transportation network. If such models may be constructed and their validity reasonably assured, then the predic tion of the traffic flows on future and present transportation links may be carried out by simulating future situations and then evaluating the potential benefits of alternative improvement projects. In the attempts that were made to construct mathematical models of transportation networks, the notion of equilibrium plays a central role. Suppose that the demand for transportation, that is, the number of trips that occur between the - rious origins and destinations is known. Then it is necessary to determine how these trips are attracted to the alternative routes available between origins and destinations. Knight (1924), gave a simple and intuitively clear description of the behaviour of road traffic under conditions of congestion.

The Rational Expectations Equilibrium Inventory Model

Author : Tryphon Kollintzas
Publisher : Springer Science & Business Media
ISBN 13 : 1468463748
Total Pages : 278 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis The Rational Expectations Equilibrium Inventory Model by : Tryphon Kollintzas

Download or read book The Rational Expectations Equilibrium Inventory Model written by Tryphon Kollintzas and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of six essays that develop and/or apply "rational expectations equilibrium inventory models" to study the time series behavior of production, sales, prices, and inventories at the industry level. By "rational expectations equilibrium inventory model" I mean the extension of the inventory model of Holt, Modigliani, Muth, and Simon (1960) to account for: (i) discounting, (ii) infinite horizon planning, (iii) observed and unobserved by the "econometrician" stochastic shocks in the production, factor adjustment, storage, and backorders management processes of firms, as well as in the demand they face for their products; and (iv) rational expectations. As is well known according to the Holt et al. model firms hold inventories in order to: (a) smooth production, (b) smooth production changes, and (c) avoid stockouts. Following the work of Zabel (1972), Maccini (1976), Reagan (1982), and Reagan and Weitzman (1982), Blinder (1982) laid the foundations of the rational expectations equilibrium inventory model. To the three reasons for holding inventories in the model of Holt et al. was added (d) optimal pricing. Moreover, the popular "accelerator" or "partial adjustment" inventory behavior equation of Lovell (1961) received its microfoundations and thus overcame the "Lucas critique of econometric modelling.

Some Aspects of the Foundations of General Equilibrium Theory

Author : P.J. Kalman
Publisher : Springer Science & Business Media
ISBN 13 : 364295331X
Total Pages : 174 pages
Book Rating : 4.6/5 (429 download)

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Book Synopsis Some Aspects of the Foundations of General Equilibrium Theory by : P.J. Kalman

Download or read book Some Aspects of the Foundations of General Equilibrium Theory written by P.J. Kalman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a wide number of economic problems the equilibrium values of the variables can be regarded as solutions of a parametrized constrained maximization problem. This occurs in static as well as dynamic models; in the latter case the choice variables are often paths in certain function spaces and thus can be regarded as points in infinite dimensional spaces. It is sometimes possible to determine qualitative properties of the solutions with respect to changes in the parameters of the model. The study of such properties is often called comparative statics; [15], [2], and [10]. Certain comparative static properties of the maxima have proven to be of particular importance for economic theory, since the works of Slutsky, Hicks, and Samuelson [15]: they have been for- lated in terms of synunetry and negative semidefiniteness of a matrix, called the Slutsky-Hicks-Samuelson matrix. A discussion of this matrix and its applications is given in Section 1. The study of these properties in economic theory, however, has so far been restricted to static models where the choice variable and the parameters are elements in Euclidean spaces, and where there is only one constraint.

Variational Inequalities and Network Equilibrium Problems

Author : F. Giannessi
Publisher : Springer Science & Business Media
ISBN 13 : 1489913580
Total Pages : 304 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Variational Inequalities and Network Equilibrium Problems by : F. Giannessi

Download or read book Variational Inequalities and Network Equilibrium Problems written by F. Giannessi and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings forth a set of papers presented at the conference on "Varia tional Inequalities and network equilibrium problems", held in Erice at the "G. Stam pacchia" School of the "E. Majorana" Centre for Scientific Culture in the period 19~25 June 1994. The meeting was conceived to contribute to the exchange between Variational Analysis and equilibrium problems, especially those related to network design. Most of the approaches and viewpoints of these fields are present in the volume, both as concerns the theory and the applications of equilibrium problems to transportation, computer and electric networks, to market behavior, and to bi~level programming. Being convinced of the great importance of equilibrium problems as well as of their complexity, the organizers hope that the merging of points of view coming from differ ent fields will stimulate theoretical research and applications. In this context Variational and Quasi~Variational Inequalities have shown them selves to be very important models for equilibrium problems. As a consequence in the last two decades they have received a lot of attention both as to mathematical inves tigation and applications. The proof that the above mentioned equilibrium problems can be expressed, in terms of Variational or Quasi~Variational Inequalities also in the non~standard and non~symmetric cases, has been a crucial improvement.

The Traffic Assignment Problem

Author : Michael Patriksson
Publisher : Courier Dover Publications
ISBN 13 : 0486802272
Total Pages : 244 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis The Traffic Assignment Problem by : Michael Patriksson

Download or read book The Traffic Assignment Problem written by Michael Patriksson and published by Courier Dover Publications. This book was released on 2015-01-19 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Numerical Methods in Economics

Author : Kenneth L. Judd
Publisher : MIT Press
ISBN 13 : 9780262100717
Total Pages : 662 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Numerical Methods in Economics by : Kenneth L. Judd

Download or read book Numerical Methods in Economics written by Kenneth L. Judd and published by MIT Press. This book was released on 1998-09-28 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: To harness the full power of computer technology, economists need to use a broad range of mathematical techniques. In this book, Kenneth Judd presents techniques from the numerical analysis and applied mathematics literatures and shows how to use them in economic analyses. The book is divided into five parts. Part I provides a general introduction. Part II presents basics from numerical analysis on R^n, including linear equations, iterative methods, optimization, nonlinear equations, approximation methods, numerical integration and differentiation, and Monte Carlo methods. Part III covers methods for dynamic problems, including finite difference methods, projection methods, and numerical dynamic programming. Part IV covers perturbation and asymptotic solution methods. Finally, Part V covers applications to dynamic equilibrium analysis, including solution methods for perfect foresight models and rational expectation models. A website contains supplementary material including programs and answers to exercises.

Nonlinear Approaches in Engineering Applications

Author : Liming Dai
Publisher : Springer Science & Business Media
ISBN 13 : 1461414687
Total Pages : 561 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Nonlinear Approaches in Engineering Applications by : Liming Dai

Download or read book Nonlinear Approaches in Engineering Applications written by Liming Dai and published by Springer Science & Business Media. This book was released on 2011-12-21 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Approaches in Engineering Applications focuses on nonlinear phenomena that are common in the engineering field. The nonlinear approaches described in this book provide a sound theoretical base and practical tools to design and analyze engineering systems with high efficiency and accuracy and with less energy and downtime. Presented here are nonlinear approaches in areas such as dynamic systems, optimal control and approaches in nonlinear dynamics and acoustics. Coverage encompasses a wide range of applications and fields including mathematical modeling and nonlinear behavior as applied to microresonators, nanotechnologies, nonlinear behavior in soil erosion,nonlinear population dynamics, and optimization in reducing vibration and noise as well as vibration in triple-walled carbon nanotubes.

Frontiers in Applied General Equilibrium Modeling

Author : Timothy J. Kehoe
Publisher : Cambridge University Press
ISBN 13 : 1139443720
Total Pages : 452 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Frontiers in Applied General Equilibrium Modeling by : Timothy J. Kehoe

Download or read book Frontiers in Applied General Equilibrium Modeling written by Timothy J. Kehoe and published by Cambridge University Press. This book was released on 2005-01-17 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2005 volume brings together twelve papers by many of the most prominent applied general equilibrium modelers honoring Herbert Scarf, the father of equilibrium computation in economics. It deals with developments in applied general equilibrium, a field which has broadened greatly since the 1980s. The contributors discuss some traditional as well as some modern topics in the field, including non-convexities in economy-wide models, tax policy, developmental modeling and energy modeling. The book also covers a range of distinct approaches, conceptual issues and computational algorithms, such as calibration and areas of application such as macroeconomics of real business cycles and finance. An introductory chapter written by the editors maps out issues and scenarios for the future evolution of applied general equilibrium.

Physical Models and Equilibrium Methods in Programming and Economics

Author : B.S. Razumikhin
Publisher : Springer Science & Business Media
ISBN 13 : 9400962746
Total Pages : 365 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Physical Models and Equilibrium Methods in Programming and Economics by : B.S. Razumikhin

Download or read book Physical Models and Equilibrium Methods in Programming and Economics written by B.S. Razumikhin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Generalized Nash Equilibrium Problems, Bilevel Programming and MPEC

Author : Didier Aussel
Publisher : Springer
ISBN 13 : 981104774X
Total Pages : 134 pages
Book Rating : 4.8/5 (11 download)

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Book Synopsis Generalized Nash Equilibrium Problems, Bilevel Programming and MPEC by : Didier Aussel

Download or read book Generalized Nash Equilibrium Problems, Bilevel Programming and MPEC written by Didier Aussel and published by Springer. This book was released on 2018-04-03 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses three classes of problems: the generalized Nash equilibrium problems, the bilevel problems and the mathematical programming with equilibrium constraints (MPEC). These problems interact through their mathematical analysis as well as their applications. The primary aim of the book is to present the modern tool of variational analysis and optimization, which are used to analyze these three classes of problems. All contributing authors are respected academicians, scientists and researchers from around the globe. These contributions are based on the lectures delivered by experts at CIMPA School, held at the University of Delhi, India, from 25 November–6 December 2013, and peer-reviewed by international experts. The book contains five chapters. Chapter 1 deals with nonsmooth, nonconvex bilevel optimization problems whose feasible set is described by using the graph of the solution set mapping of a parametric optimization problem. Chapter 2 describes a constraint qualification to MPECs considered as an application of calmness concept of multifunctions and is used to derive M-stationarity conditions for MPEC. Chapter 3 discusses the first- and second-order optimality conditions derived for a special case of a bilevel optimization problem in which the constraint set of the lower level problem is described as a general compact convex set. Chapter 4 concentrates the results of the modelization and analysis of deregulated electricity markets with a focus on auctions and mechanism design. Chapter 5 focuses on optimization approaches called reflection methods for protein conformation determination within the framework of matrix completion. The last chapter (Chap. 6) deals with the single-valuedness of quasimonotone maps by using the concept of single-directionality with a special focus on the case of the normal operator of lower semi-continuous quasiconvex functions.