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Author: Anna Nagurney
Publisher: Springer Science & Business Media
ISBN: 146152301X
Category : Business & Economics
Languages : en
Pages : 312
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Book Description
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.
Author: Anna Nagurney
Publisher: Springer Science & Business Media
ISBN: 146152301X
Category : Business & Economics
Languages : en
Pages : 312
Get Book Here
Book Description
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.
Author: Anna Nagurney
Publisher: Springer Science & Business Media
ISBN: 9780792396376
Category : Business & Economics
Languages : en
Pages : 328
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Book Description
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.
Author: Anna Nagurney
Publisher: Springer Science & Business Media
ISBN: 1475730055
Category : Business & Economics
Languages : en
Pages : 423
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Book Description
Since the publication of the first edition of Network Economics: A Variational Inequality Approach in 1993, there have been many ad vances in both methodological developments, as well as, applications in this field. These have occurred in an environment of an increasingly networked global economy, in which the importance of transportation networks and communication networks is now well-recognized, with net works such as knowledge networks, environmental networks, and finan cial networks receiving growing attention. This edition adds recent research progress in new and evolving ar eas of network economics through common and unifying principles. In addition, it includes dynamic models of traffic, of spatially separated markets, of oligopolistic markets, and of financial markets. In order to expand the range and reach of this material, we have also included a series of problems in an appendix for self-study purposes and for use in the classroom. We note that computational economics has been at the forefront in stimulating the development of mathematical methodologies for the analysis and solution of complex, large-scale problems. The past fifteen years, in particular, have witnessed a dramatic growth of interest in this area. Supported by the increasing availability of data and by advances in computer architectures, the scale and dimensions of problems that can now be handled are unveiling new horizons in both theoretical modeling and policy analysis.
Author: Christodoulos A. Floudas
Publisher: Springer Science & Business Media
ISBN: 0387747583
Category : Mathematics
Languages : en
Pages : 4646
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Book Description
The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".
Author: Nicholas J. Daras
Publisher: Springer Nature
ISBN: 3030446255
Category : Mathematics
Languages : en
Pages : 564
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Book Description
This volume presents a broad discussion of computational methods and theories on various classical and modern research problems from pure and applied mathematics. Readers conducting research in mathematics, engineering, physics, and economics will benefit from the diversity of topics covered. Contributions from an international community treat the following subjects: calculus of variations, optimization theory, operations research, game theory, differential equations, functional analysis, operator theory, approximation theory, numerical analysis, asymptotic analysis, and engineering. Specific topics include algorithms for difference of monotone operators, variational inequalities in semi-inner product spaces, function variation principles and normed minimizers, equilibria of parametrized N-player nonlinear games, multi-symplectic numerical schemes for differential equations, time-delay multi-agent systems, computational methods in non-linear design of experiments, unsupervised stochastic learning, asymptotic statistical results, global-local transformation, scattering relations of elastic waves, generalized Ostrowski and trapezoid type rules, numerical approximation, Szász Durrmeyer operators and approximation, integral inequalities, behaviour of the solutions of functional equations, functional inequalities in complex Banach spaces, functional contractions in metric spaces.
Author: F. Giannessi
Publisher: Springer Science & Business Media
ISBN: 9780387242095
Category : Mathematics
Languages : en
Pages : 1348
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Book Description
This book discusses a new discipline, variational analysis, which contains the calculus of variations, differential calculus, optimization, and variational inequalities. To such classic branches of mathematics, variational analysis provides a uniform theoretical base that represents a powerful tool for the applications. The contributors are among the best experts in the field. Audience The target audience of this book includes scholars in mathematics (especially those in mathematical analysis), mathematical physics and applied mathematics, calculus of variations, optimization and operations research, industrial mathematics, structural engineering, and statistics and economics.
Author: Liqun Qi
Publisher: Springer Science & Business Media
ISBN: 9780387242545
Category : Mathematics
Languages : en
Pages : 618
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Book Description
This book contains refereed papers which were presented at the 34th Workshop of the International School of Mathematics "G. Stampacchia,” the International Workshop on Optimization and Control with Applications. The book contains 28 papers that are grouped according to four broad topics: duality and optimality conditions, optimization algorithms, optimal control, and variational inequality and equilibrium problems. The specific topics covered in the individual chapters include optimal control, unconstrained and constrained optimization, complementarity and variational inequalities, equilibrium problems, semi-definite programs, semi-infinite programs, matrix functions and equations, nonsmooth optimization, generalized convexity and generalized monotinicity, and their applications. Audience This book is suitable for researchers, practitioners, and postgraduate students in optimization, operations research, and optimal control.
Author: F. Giannessi
Publisher: Springer Science & Business Media
ISBN: 0306480263
Category : Mathematics
Languages : en
Pages : 304
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Book Description
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: Zhang Wenpeng
Publisher: Infinite Study
ISBN: 1599730812
Category :
Languages : en
Pages : 130
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Book Description
Papers on an equation involving the Smarandache function and its positive integer solutions, the Smarandache kn-digital subsequence, the Smarandache 3n-digital sequence and the Zhang Wenpeng's conjecture, the quintic supported spline wavelets with numerical integration and similar topics. Contributors: A. A. Majumdar, B. Chen, C. Shi, S. Wang, L. Zhang, A. Saeid, M. Haveshki, T. Veluchamy, P.S.Sivakkumar, and others.
Author: Michael Ulbrich
Publisher: SIAM
ISBN: 1611970687
Category : Mathematics
Languages : en
Pages : 315
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Book Description
A comprehensive treatment of semismooth Newton methods in function spaces: from their foundations to recent progress in the field. This book is appropriate for researchers and practitioners in PDE-constrained optimization, nonlinear optimization and numerical analysis, as well as engineers interested in the current theory and methods for solving variational inequalities.
