Nonlinear Programming Techniques For Equilibria

Author : Giancarlo Bigi,Marco Castellani,Massimo Pappalardo,Mauro Passacantando
Publisher : Springer
Page : 120 pages
File Size : 41,7 Mb
Release : 2018-09-20
Category : Business & Economics
ISBN : 9783030002053

Get Book

Nonlinear Programming Techniques for Equilibria by Giancarlo Bigi,Marco Castellani,Massimo Pappalardo,Mauro Passacantando Pdf

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.

Author : B.S. Razumikhin
Publisher : Springer Science & Business Media
Page : 365 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400962743

Get Book

Physical Models and Equilibrium Methods in Programming and Economics by B.S. Razumikhin Pdf

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.

Author : F. Giannessi,A. Maugeri,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 44,7 Mb
Release : 2006-04-11
Category : Mathematics
ISBN : 9780306480263

Get Book

Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models by F. Giannessi,A. Maugeri,Panos M. Pardalos Pdf

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.

Author : Zaifu Yang
Publisher : Springer Science & Business Media
Page : 349 pages
File Size : 44,8 Mb
Release : 2013-04-17
Category : Business & Economics
ISBN : 9781475748390

Get Book

Computing Equilibria and Fixed Points by Zaifu Yang Pdf

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).

Author : James Harold Bigelow,Stanford University. Department of Operations Research. Operations Research House
Publisher : Unknown
Page : 76 pages
File Size : 46,6 Mb
Release : 1968
Category : Chemical equilibrium
ISBN : STANFORD:36105046359894

Get Book

The Chemical Equilibrium Problem by James Harold Bigelow,Stanford University. Department of Operations Research. Operations Research House Pdf

It has long been known that the problem of determining the equilibrium composition of a solution of chemically reacting species could be formulated as a constrained minimum problem. Previous methods for solving the chemical equilibrium problem in this form have had much success. However, all such methods run into trouble whenever degeneracy or near-degeneracy occurs during the computational procedure. The paper shows that the constrained minimum formulation of the chemical equilibrium problem is equivalent to a generalized linear program which can in turn be replaced by a quadratic program. In these alternative forms, degeneracy is more easily accomodated than in previous methods. (Author).

Author : M.A. Florian
Publisher : Springer Science & Business Media
Page : 457 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642481239

Get Book

Traffic Equilibrium Methods by M.A. Florian Pdf

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.

Author : Jiri Outrata,M. Kocvara,J. Zowe
Publisher : Springer Science & Business Media
Page : 281 pages
File Size : 52,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475728255

Get Book

Nonsmooth Approach to Optimization Problems with Equilibrium Constraints by Jiri Outrata,M. Kocvara,J. Zowe Pdf

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.

Author : E. N. Barron
Publisher : John Wiley & Sons
Page : 574 pages
File Size : 46,7 Mb
Release : 2013-04-22
Category : Business & Economics
ISBN : 9781118216934

Get Book

Game Theory by E. N. Barron Pdf

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 Maple™, 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.

Author : Timothy J. Kehoe,T. N. Srinivasan,John Whalley
Publisher : Cambridge University Press
Page : 452 pages
File Size : 44,5 Mb
Release : 2005-01-17
Category : Business & Economics
ISBN : 9781139443722

Get Book

Frontiers in Applied General Equilibrium Modeling by Timothy J. Kehoe,T. N. Srinivasan,John Whalley Pdf

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.

Author : Alexander Krylatov,Victor Zakharov,Tero Tuovinen
Publisher : Springer Nature
Page : 231 pages
File Size : 54,6 Mb
Release : 2019-11-26
Category : Technology & Engineering
ISBN : 9783030341022

Get Book

Optimization Models and Methods for Equilibrium Traffic Assignment by Alexander Krylatov,Victor Zakharov,Tero Tuovinen Pdf

This book is focused on the discussion of the traffic assignment problem, the mathematical and practical meaning of variables, functions and basic principles. This work gives information about new approaches, methods and algorithms based on original methodological technique, developed by authors in their publications for the past several years, as well as corresponding prospective implementations. The book may be of interest to a wide range of readers, such as civil engineering students, traffic engineers, developers of traffic assignment algorithms etc. The obtained results here are to be used in both practice and theory. This book is devoted to the traffic assignment problem, formulated in a form of nonlinear optimization program. The most efficient solution algorithms related to the problem are based on its structural features and practical meaning rather than on standard nonlinear optimization techniques or approaches. The authors have carefully considered the meaning of the traffic assignment problem for efficient algorithms development.

Author : Tan C. Miller,Terry L. Friesz,Roger L. Tobin
Publisher : Springer Science & Business Media
Page : 247 pages
File Size : 49,7 Mb
Release : 2013-04-18
Category : Science
ISBN : 9783662032800

Get Book

Equilibrium Facility Location on Networks by Tan C. Miller,Terry L. Friesz,Roger L. Tobin Pdf

This is a book about the simultaneous location, production and distri bution decisions of a firm entering a competitive market whose spatial nature is describable by a network in which the market either achieves an equilibrium or is equilibrium tending. As such, the problem is of clear theoretical and practical importance, for it is a rather general version of the problem faced by real firms every day in deciding where to locate. Further, the timeliness of this subject manifests itself in the growing excitement and interest found both in the research/academic communities and in the practitioner/private industry communities for more comprehensive approaches to competitive facility location analy sis and equilibrium modeling of networks. The desire both for new conceptual approaches yielding enhanced insights and for practical methodologies to capture these insights drives this interest. While nor mative, deterministic facility location modeling techniques currently provide valuable input into the location decision-making process, re searchers and practitioners alike have realized the vast and relatively untapped potential of more advanced location decision making tech niques. In this book, we develop what we believe represents a major new line of research in the field of competitive facility location analysis; namely, equilibrium facility location modeling. In particular, this book offers a number of innovations in the mathe matical analysis and computation of solutions to location models which we have pioneered and which are collected under a single cover for the first time.

Author : Julio B. Clempner,Alexander Poznyak
Publisher : Springer Nature
Page : 340 pages
File Size : 42,9 Mb
Release : 2023-12-13
Category : Technology & Engineering
ISBN : 9783031435751

Get Book

Optimization and Games for Controllable Markov Chains by Julio B. Clempner,Alexander Poznyak Pdf

This book considers a class of ergodic finite controllable Markov's chains. The main idea behind the method, described in this book, is to develop the original discrete optimization problems (or game models) in the space of randomized formulations, where the variables stand in for the distributions (mixed strategies or preferences) of the original discrete (pure) strategies in the use. The following suppositions are made: a finite state space, a limited action space, continuity of the probabilities and rewards associated with the actions, and a necessity for accessibility. These hypotheses lead to the existence of an optimal policy. The best course of action is always stationary. It is either simple (i.e., nonrandomized stationary) or composed of two nonrandomized policies, which is equivalent to randomly selecting one of two simple policies throughout each epoch by tossing a biased coin. As a bonus, the optimization procedure just has to repeatedly solve the time-average dynamic programming equation, making it theoretically feasible to choose the optimum course of action under the global restriction. In the ergodic cases the state distributions, generated by the corresponding transition equations, exponentially quickly converge to their stationary (final) values. This makes it possible to employ all widely used optimization methods (such as Gradient-like procedures, Extra-proximal method, Lagrange's multipliers, Tikhonov's regularization), including the related numerical techniques. In the book we tackle different problems and theoretical Markov models like controllable and ergodic Markov chains, multi-objective Pareto front solutions, partially observable Markov chains, continuous-time Markov chains, Nash equilibrium and Stackelberg equilibrium, Lyapunov-like function in Markov chains, Best-reply strategy, Bayesian incentive-compatible mechanisms, Bayesian Partially Observable Markov Games, bargaining solutions for Nash and Kalai-Smorodinsky formulations, multi-traffic signal-control synchronization problem, Rubinstein's non-cooperative bargaining solutions, the transfer pricing problem as bargaining.

Author : P. Daniele,F. Giannessi,A. Maugeri
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 50,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461302391

Get Book

Equilibrium Problems and Variational Models by P. Daniele,F. Giannessi,A. Maugeri Pdf

The volume, devoted to variational analysis and its applications, collects selected and refereed contributions, which provide an outline of the field. The meeting of the title "Equilibrium Problems and Variational Models", which was held in Erice (Sicily) in the period June 23 - July 2 2000, was the occasion of the presentation of some of these papers; other results are a consequence of a fruitful and constructive atmosphere created during the meeting. New results, which enlarge the field of application of variational analysis, are presented in the book; they deal with the vectorial analysis, time dependent variational analysis, exact penalization, high order deriva tives, geometric aspects, distance functions and log-quadratic proximal methodology. The new theoretical results allow one to improve in a remarkable way the study of significant problems arising from the applied sciences, as continuum model of transportation, unilateral problems, multicriteria spatial price models, network equilibrium problems and many others. As noted in the previous book "Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models", edited by F. Giannessi, A. Maugeri and P.M. Pardalos, Kluwer Academic Publishers, Vol. 58 (2001), the progress obtained by variational analysis has permitted to han dle problems whose equilibrium conditions are not obtained by the mini mization of a functional. These problems obey a more realistic equilibrium condition expressed by a generalized orthogonality (complementarity) con dition, which enriches our knowledge of the equilibrium behaviour. Also this volume presents important examples of this formulation.

Author : Jerome Bracken,Garth P. McCormick
Publisher : New York : Wiley
Page : 136 pages
File Size : 43,8 Mb
Release : 1968
Category : Mathematics
ISBN : UCAL:B4407391

Get Book

Selected Applications of Nonlinear Programming by Jerome Bracken,Garth P. McCormick Pdf

Author : Zhi-Quan Luo,Jong-Shi Pang,Daniel Ralph
Publisher : Cambridge University Press
Page : 128 pages
File Size : 41,7 Mb
Release : 1996-11-13
Category : Mathematics
ISBN : 9781316582619

Get Book

Mathematical Programs with Equilibrium Constraints by Zhi-Quan Luo,Jong-Shi Pang,Daniel Ralph Pdf

This book provides a solid foundation and an extensive study for an important class of constrained optimization problems known as Mathematical Programs with Equilibrium Constraints (MPEC), which are extensions of bilevel optimization problems. The book begins with the description of many source problems arising from engineering and economics that are amenable to treatment by the MPEC methodology. Error bounds and parametric analysis are the main tools to establish a theory of exact penalisation, a set of MPEC constraint qualifications and the first-order and second-order optimality conditions. The book also describes several iterative algorithms such as a penalty-based interior point algorithm, an implicit programming algorithm and a piecewise sequential quadratic programming algorithm for MPECs. Results in the book are expected to have significant impacts in such disciplines as engineering design, economics and game equilibria, and transportation planning, within all of which MPEC has a central role to play in the modelling of many practical problems.