The Equilibrium Problem And Applications
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| Author | : Gábor Kassay |
| Publisher | : Academic Press |
| Total Pages | : 442 |
| Release | : 2018-10-09 |
| Genre | : Business & Economics |
| ISBN | : 0128110309 |
Equilibrium Problems and Applications develops a unified variational approach to deal with single-valued, set-valued and quasi-equilibrium problems. The authors promote original results in relationship with classical contributions to the field of equilibrium problems. The content evolved in the general setting of topological vector spaces and it lies at the interplay between pure and applied nonlinear analysis, mathematical economics, and mathematical physics. This abstract approach is based on tools from various fields, including set-valued analysis, variational and hemivariational inequalities, fixed point theory, and optimization. Applications include models from mathematical economics, Nash equilibrium of non-cooperative games, and Browder variational inclusions. The content is self-contained and the book is mainly addressed to researchers in mathematics, economics and mathematical physics as well as to graduate students in applied nonlinear analysis. - A rigorous mathematical analysis of Nash equilibrium type problems, which play a central role to describe network traffic models, competition games or problems arising in experimental economics - Develops generic models relevant to mathematical economics and quantitative modeling of game theory, aiding economists to understand vital material without having to wade through complex proofs - Reveals a number of surprising interactions among various equilibria topics, enabling readers to identify a common and unified approach to analysing problem sets - Illustrates the deep features shared by several types of nonlinear problems, encouraging readers to develop further this unifying approach from other viewpoints into economic models in turn
| Author | : P. Daniele |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 468 |
| Release | : 2003-06-30 |
| Genre | : Mathematics |
| ISBN | : 9781402074707 |
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 | : F. Giannessi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 304 |
| Release | : 2006-04-11 |
| Genre | : Mathematics |
| ISBN | : 0306480263 |
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 | : Steven S. Zumdahl |
| Publisher | : Brooks Cole |
| Total Pages | : 212 |
| Release | : 1989 |
| Genre | : Mathematics |
| ISBN | : 9780669167184 |
| Author | : Jiri Outrata |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 281 |
| Release | : 2013-06-29 |
| Genre | : Mathematics |
| ISBN | : 1475728255 |
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 | : Yeol Je Cho |
| Publisher | : Nova Publishers |
| Total Pages | : 200 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 9781594548741 |
The aim of this volume is to introduce and exchange recent new topics on the areas of inequality theory and their applications dealing in pure and applied mathematics.
| Author | : Panos M. Pardalos |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 502 |
| Release | : 2009-10-20 |
| Genre | : Business & Economics |
| ISBN | : 1441901582 |
The chapters in this volume, written by international experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician. These contributions focus on recent developments in complementarity theory, variational principles, stability theory of functional equations, nonsmooth optimization, and several other important topics at the forefront of nonlinear analysis and optimization.
| Author | : Christodoulos A. Floudas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 4646 |
| Release | : 2008-09-04 |
| Genre | : Mathematics |
| ISBN | : 0387747583 |
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 | : Ally Hu |
| Publisher | : CRC Press |
| Total Pages | : 568 |
| Release | : 2015-06-11 |
| Genre | : Computers |
| ISBN | : 1315684985 |
The 2014 Asia-Pacific Conference on Computer Science and Applications was held in Shanghai, December 27-28, 2014. These CSAC-2014 proceedings include 105 selected papers, which focus not only on the research of science and technology of computer sciences, but also on the research of applications, aiming at a quick and immediate effect on
| Author | : Larry S Karp |
| Publisher | : World Scientific |
| Total Pages | : 303 |
| Release | : 2021-12-08 |
| Genre | : Business & Economics |
| ISBN | : 9811249881 |
Lecture Notes in International Trade Theory covers classical international trade models (including the Ricardian, Ricardo Viner, and Heckscher-Ohlin-Samuelson models). The course is designed for M.Sc. and first year PhD students. It relies on both graphical and analytic methods, requiring only intermediate microeconomics and a solid grounding in calculus. The material emphasizes 'second-best' settings, where markets are imperfect. The goal is to equip students with a good enough understanding of open-economy general equilibrium relations that they understand how distortions ripple across different markets, e.g. commodity and factor markets. The Author applies these ideas to environmental and natural resource problems, including pollution 'leakage' (where pollution reductions in one country are offset by trading partners' increased pollution) and imperfect property rights. Other applications include the general equilibrium effects of commodity and trade taxes, international transfers (the 'transfer problem'), minimum wage constraints, and immiserizing growth. The Author assumes that students have some experience in formulating and answering comparative statics questions in an optimization setting. Building on these skills, and developing the idea of stability in an equilibrium setting (the Marshall Lerner condition), students learn how to formulate and answer comparative static questions in trade models.
