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Equilibrium Models and Variational Inequalities

Equilibrium Models and Variational Inequalities Author Igor Konnov
ISBN-10 0080471382
Release 2007-02-08
Pages 250
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The concept of equilibrium plays a central role in various applied sciences, such as physics (especially, mechanics), economics, engineering, transportation, sociology, chemistry, biology and other fields. If one can formulate the equilibrium problem in the form of a mathematical model, solutions of the corresponding problem can be used for forecasting the future behavior of very complex systems and, also, for correcting the the current state of the system under control. This book presents a unifying look on different equilibrium concepts in economics, including several models from related sciences. - Presents a unifying look on different equilibrium concepts and also the present state of investigations in this field - Describes static and dynamic input-output models, Walras, Cassel-Wald, spatial price, auction market, oligopolistic equilibrium models, transportation and migration equilibrium models - Covers the basics of theory and solution methods both for the complementarity and variational inequality problems - The methods are illustrated by applications and exercises to economic equilibrium models



Finite Dimensional Variational Inequalities and Complementarity Problems

Finite Dimensional Variational Inequalities and Complementarity Problems Author Francisco Facchinei
ISBN-10 9780387218151
Release 2007-06-04
Pages 704
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This is part two of a two-volume work presenting a comprehensive treatment of the finite-dimensional variational inequality and complementarity problem. It details algorithms for solving finite dimensional variational inequalities and complementarity problems. Coverage includes abundant exercises as well as an extensive bibliography. The book will be an enduring reference on the subject and provide the foundation for its sustained growth.



Stochastic Modelling in Process Technology

Stochastic Modelling in Process Technology Author Herold G. Dehling
ISBN-10 0080548970
Release 2007-07-03
Pages 290
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There is an ever increasing need for modelling complex processes reliably. Computational modelling techniques, such as CFD and MD may be used as tools to study specific systems, but their emergence has not decreased the need for generic, analytical process models. Multiphase and multicomponent systems, and high-intensity processes displaying a highly complex behaviour are becoming omnipresent in the processing industry. This book discusses an elegant, but little-known technique for formulating process models in process technology: stochastic process modelling. The technique is based on computing the probability distribution for a single particle's position in the process vessel, and/or the particle's properties, as a function of time, rather than - as is traditionally done - basing the model on the formulation and solution of differential conservation equations. Using this technique can greatly simplify the formulation of a model, and even make modelling possible for processes so complex that the traditional method is impracticable. Stochastic modelling has sporadically been used in various branches of process technology under various names and guises. This book gives, as the first, an overview of this work, and shows how these techniques are similar in nature, and make use of the same basic mathematical tools and techniques. The book also demonstrates how stochastic modelling may be implemented by describing example cases, and shows how a stochastic model may be formulated for a case, which cannot be described by formulating and solving differential balance equations. Introduction to stochastic process modelling as an alternative modelling technique Shows how stochastic modelling may be succesful where the traditional technique fails Overview of stochastic modelling in process technology in the research literature Illustration of the principle by a wide range of practical examples In-depth and self-contained discussions Points the way to both mathematical and technological research in a new, rewarding field



Proceedings of the Seventh International Conference on Management Science and Engineering Management

Proceedings of the Seventh International Conference on Management Science and Engineering Management Author Jiuping Xu
ISBN-10 9783642400810
Release 2013-09-25
Pages 1542
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This book presents the proceedings of the Seventh International Conference on Management Science and Engineering Management (ICMSEM2013) held from November 7 to 9, 2013 at Drexel University, Philadelphia, Pennsylvania, USA and organized by the International Society of Management Science and Engineering Management, Sichuan University (Chengdu, China) and Drexel University (Philadelphia, Pennsylvania, USA). The goals of the Conference are to foster international research collaborations in Management Science and Engineering Management as well as to provide a forum to present current research findings. The selected papers cover various areas in management science and engineering management, such as Decision Support Systems, Multi-Objective Decisions, Uncertain Decisions, Computational Mathematics, Information Systems, Logistics and Supply Chain Management, Relationship Management, Scheduling and Control, Data Warehousing and Data Mining, Electronic Commerce, Neural Networks, Stochastic Models and Simulation, Fuzzy Programming, Heuristics Algorithms, Risk Control, Organizational Behavior, Green Supply Chains, and Carbon Credits. The proceedings introduce readers to novel ideas on and different problem-solving methods in Management Science and Engineering Management. We selected excellent papers from all over the world, integrating their expertise and ideas in order to improve research on Management Science and Engineering Management.



Mathematical and Computational Approaches in Advancing Modern Science and Engineering

Mathematical and Computational Approaches in Advancing Modern Science and Engineering Author Jacques Bélair
ISBN-10 9783319303796
Release 2016-08-10
Pages 806
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Focusing on five main groups of interdisciplinary problems, this book covers a wide range of topics in mathematical modeling, computational science and applied mathematics. It presents a wealth of new results in the development of modeling theories and methods, advancing diverse areas of applications and promoting interdisciplinary interactions between mathematicians, scientists, engineers and representatives from other disciplines. The book offers a valuable source of methods, ideas, and tools developed for a variety of disciplines, including the natural and social sciences, medicine, engineering, and technology. Original results are presented on both the fundamental and applied level, accompanied by an ample number of real-world problems and examples emphasizing the interdisciplinary nature and universality of mathematical modeling, and providing an excellent outline of today’s challenges. Mathematical modeling, with applied and computational methods and tools, plays a fundamental role in modern science and engineering. It provides a primary and ubiquitous tool in the context making new discoveries, as well as in the development of new theories and techniques for solving key problems arising in scientific and engineering applications. The contributions, which are the product of two highly successful meetings held jointly in Waterloo, Ontario, Canada on the main campus of Wilfrid Laurier University in June 2015, i.e. the International Conference on Applied Mathematics, Modeling and Computational Science, and the Annual Meeting of the Canadian Applied and Industrial Mathematics (CAIMS), make the book a valuable resource for any reader interested in a broader overview of the methods, ideas and tools involved in mathematical and computational approaches developed for other disciplines, including the natural and social sciences, engineering and technology.



Equilibrium Problems Nonsmooth Optimization and Variational Inequality Models

Equilibrium Problems  Nonsmooth Optimization and Variational Inequality Models Author Franco Giannessi
ISBN-10 9780306480263
Release 2006-04-11
Pages 304
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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.



Optimization in Science and Engineering

Optimization in Science and Engineering Author Themistocles Rassias
ISBN-10 9781493908080
Release 2014-05-29
Pages 610
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Optimization in Science and Engineering is dedicated in honor of the 60th birthday of Distinguished Professor Panos M. Pardalos. Pardalos’s past and ongoing work has made a significant impact on several theoretical and applied areas in modern optimization. As tribute to the diversity of Dr. Pardalos’s work in Optimization, this book comprises a collection of contributions from experts in various fields of this rich and diverse area of science. Topics highlight recent developments and include: Deterministic global optimization Variational inequalities and equilibrium problems Approximation and complexity in numerical optimization Non-smooth optimization Statistical models and data mining Applications of optimization in medicine, energy systems, and complex network analysis This volume will be of great interest to graduate students, researchers, and practitioners, in the fields of optimization and engineering.



Proceedings of the Ninth International Conference on Management Science and Engineering Management

Proceedings of the Ninth International Conference on Management Science and Engineering Management Author Jiuping Xu
ISBN-10 9783662472415
Release 2015-05-20
Pages 1600
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This is the Proceedings of the Ninth International Conference on Management Science and Engineering Management (ICMSEM) held from July 21-23, 2015 at Karlsruhe, Germany. The goals of the conference are to foster international research collaborations in Management Science and Engineering Management as well as to provide a forum to present current findings. These proceedings cover various areas in management science and engineering management. It focuses on the identification of management science problems in engineering and innovatively using management theory and methods to solve engineering problems effectively. It also establishes a new management theory and methods based on experience of new management issues in engineering. Readers interested in the fields of management science and engineering management will benefit from the latest cutting-edge innovations and research advances presented in these proceedings and will find new ideas and research directions. A total number of 132 papers from 15 countries are selected for the proceedings by the conference scientific committee through rigorous referee review. The selected papers in the first volume are focused on Intelligent System and Management Science covering areas of Intelligent Systems, Logistics Engineering, Information Technology and Risk Management. The selected papers in the second volume are focused on Computing and Engineering Management covering areas of Computing Methodology, Project Management, Industrial Engineering and Decision Making Systems.



Proceedings of the Sixth International Conference on Management Science and Engineering Management

Proceedings of the Sixth International Conference on Management Science and Engineering Management Author Jiuping Xu
ISBN-10 9781447146001
Release 2012-09-25
Pages 1062
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Welcome to the proceedings of the Sixth International Conference on Management Science and Engineering Management (ICMSEM2012) held from November 11 to 14, 2012 at Quaid-i-Azam University, Islamabad, Pakistan and supported by Sichuan University (Chengdu, China), Quaid-i-Azam University (Islamabad, Pakistan) and The National Natural Science Foundation of China. The International Conference on Management Science and Engineering Management is the annual conference organized by the International Society of Management Science and Engineering Management. The goals of the Conference are to foster international research collaborations in Management Science and Engineering Management as well as to provide a forum to present current research results. The papers are classified into 8 sections: Computer and Networks, Information Technology, Decision Support System, Industrial Engineering, Supply Chain Management, Project Management, Manufacturing and Ecological Engineering. The key issues of the sixth ICMSEM cover various areas in MSEM, such as Decision Support System, Computational Mathematics, Information Systems, Logistics and Supply Chain Management, Relationship Management, Scheduling and Control, Data Warehousing and Data Mining, Electronic Commerce, Neural Networks, Stochastic models and Simulation, Heuristics Algorithms, Risk Control, and Carbon Credits.



Numerical Time Dependent Partial Differential Equations for Scientists and Engineers

Numerical Time Dependent Partial Differential Equations for Scientists and Engineers Author Moysey Brio
ISBN-10 0080917046
Release 2010-09-21
Pages 312
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It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc. The first three chapters focus on basic properties of partial differential equations, including analysis of the dispersion relation, symmetries, particular solutions and instabilities of the PDEs; methods of discretization and convergence theory for initial value problems. The goal is to progress from observations of simple numerical artifacts like diffusion, damping, dispersion, and anisotropies to their analysis and management technique, as it is not always possible to completely eliminate them. In the second part of the book we cover topics for which there are only sporadic theoretical results, while they are an integral part and often the most important part for successful numerical simulation. We adopt a more heuristic and practical approach using numerical methods of investigation and validation. The aim is teach students subtle key issues in order to separate physics from numerics. The following topics are addressed: Implementation of transparent and absorbing boundary conditions; Practical stability analysis in the presence of the boundaries and interfaces; Treatment of problems with different temporal/spatial scales either explicit or implicit; preservation of symmetries and additional constraints; physical regularization of singularities; resolution enhancement using adaptive mesh refinement and moving meshes. Self contained presentation of key issues in successful numerical simulation Accessible to scientists and engineers with diverse background Provides analysis of the dispersion relation, symmetries, particular solutions and instabilities of the partial differential equations



Variational and Quasi Variational Inequalities in Mechanics

Variational and Quasi Variational Inequalities in Mechanics Author Alexander S. Kravchuk
ISBN-10 9781402063770
Release 2007-09-04
Pages 337
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The essential aim of this book is to consider a wide set of problems arising in the mathematical modeling of mechanical systems under unilateral constraints. In these investigations elastic and non-elastic deformations, friction and adhesion phenomena are taken into account. All the necessary mathematical tools are given: local boundary value problem formulations, construction of variational equations and inequalities and their transition to minimization problems, existence and uniqueness theorems, and variational transformations (Friedrichs and Young-Fenchel-Moreau) to dual and saddle-point search problems.



Combined Relaxation Methods for Variational Inequalities

Combined Relaxation Methods for Variational Inequalities Author Igor Konnov
ISBN-10 3540679995
Release 2001
Pages 181
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Variational inequalities proved to be a very useful tool for investigation and solution of various equilibrium type problems arising in Economics, Operations Research, Mathematical Physics, and Transportation. This book is devoted to a new general approach to constructing solution methods for variational inequalities, which was called the combined relaxation approach. This approach is rather flexible and allows one to construct various methods both for single-valued and for multi-valued variational inequalities, including nonlinear constrained problems. The other essential feature of the combined relaxation methods is that they are convergent under very mild assumptions. The book can be viewed as an attempt to discribe the existing combined relaxation methods as a whole.



KKM Theory and Applications in Nonlinear Analysis

KKM Theory and Applications in Nonlinear Analysis Author George Xian-Zhi Yuan
ISBN-10 0824700317
Release 1999-02-09
Pages 648
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This reference provides a lucid introduction to the principles and applications of Knaster-Kuratowski-Mazurkiewicz (KKM) theory and explores related topics in nonlinear set-valued analysis.



Operations Research and Decision Aid Methodologies in Traffic and Transportation Management

Operations Research and Decision Aid Methodologies in Traffic and Transportation Management Author Martine Labbe
ISBN-10 3540646523
Release 1998-10-20
Pages 339
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This is a collection of state-of-the-art surveys on topics at the interface between transportation modeling and operations research given by leading international experts. Based on contributions to a NATO workshop, the surveys are up-to-date and rigorous presentations or applications of quantitative methods in the area. The subjects covered include dynamic traffic simulation techniques and dynamic routing in congested networks, operation and control of traffic management tools, optimized transportation data collection, and vehicle routing problems.



Projected Dynamical Systems and Variational Inequalities with Applications

Projected Dynamical Systems and Variational Inequalities with Applications Author Anna Nagurney
ISBN-10 9781461523017
Release 2012-12-06
Pages 296
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Equilibrium is a concept used in operations research and economics to understand the interplay of factors and problems arising from competitive systems in the economic world. The problems in this area are large and complex and have involved a variety of mathematical methodologies. In this monograph, the authors have widened the scope of theoretical work with a new approach, `projected dynamical systems theory', to previous work in variational inequality theory. While most classical work in this area is static, the introduction to the theory of projected dynamical systems will allow many real-life dynamic situations and problems to be handled and modeled. This monograph includes: a new theoretical approach, `projected dynamical system', which allows the researcher to model real-life situations more accurately; new mathematical methods allowing researchers to combine other theoretical approaches with the projected dynamical systems approach; a framework in which research can adequately model natural, financial and human (real life) situations in competitive equilibrium problems; the computational and numerical methods for the implementation of the methods and theory discussed in the book; stability analysis, algorithms and computational procedures are offered for each set of applications.



Vector Variational Inequalities and Vector Optimization

Vector Variational Inequalities and Vector Optimization Author Qamrul Hasan Ansari
ISBN-10 9783319630496
Release 2017-10-31
Pages 509
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This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems. It is the first-ever book to introduce well-posedness and sensitivity analysis for vector equilibrium problems. The first chapter provides basic notations and results from the areas of convex analysis, functional analysis, set-valued analysis and fixed-point theory for set-valued maps, as well as a brief introduction to variational inequalities and equilibrium problems. Chapter 2 presents an overview of analysis over cones, including continuity and convexity of vector-valued functions. The book then shifts its focus to solution concepts and classical methods in vector optimization. It describes the formulation of vector variational inequalities and their applications to vector optimization, followed by separate chapters on linear scalarization, nonsmooth and generalized vector variational inequalities. Lastly, the book introduces readers to vector equilibrium problems and generalized vector equilibrium problems. Written in an illustrative and reader-friendly way, the book offers a valuable resource for all researchers whose work involves optimization and vector optimization.



Leray Schauder Type Alternatives Complementarity Problems and Variational Inequalities

Leray   Schauder Type Alternatives  Complementarity Problems and Variational Inequalities Author George Isac
ISBN-10 9780387329000
Release 2006-08-18
Pages 352
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Complementarity theory, a relatively new domain in applied mathematics, has deep connections with several aspects of fundamental mathematics and also has many applications in optimization, economics and engineering. The study of variational inequalities is another domain of applied mathematics with many applications to the study of certain problems with unilateral conditions. This book is the first to discuss complementarity theory and variational inequalities using Leray Schauder type alternatives. The ideas and method presented in this book may be considered as a starting point for new developments.