The Study of Minimax Inequalities and Applications to Economies and Variational Inequalities

The Study of Minimax Inequalities and Applications to Economies and Variational Inequalities PDF

Author: George Xian-Zhi Yuan

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 157

ISBN-13: 0821807471

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This book provides a unified treatment for the study of the existence of equilibria of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities, which strongly depend on his infinite dimensional version of the classical Knaster, Kuratowski and Mazurkiewicz Lemma (KKM Lemma) in 1961. Studied are applications of general system versions of minimax inequalities and generalized quasi-variational inequalities, and random abstract economies and its applications to the system of random quasi-variational inequalities are given.

Study of Minimax Inequalities and Applications to Economies and Variational

Study of Minimax Inequalities and Applications to Economies and Variational PDF

Author: George Xian-Zhi Yuan

Publisher: Oxford University Press, USA

Published: 2014-09-11

Total Pages: 157

ISBN-13: 9781470402143

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This text provides a unified treatment for the study of the existence of equilibria of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities, which strongly depend on his infinite dimensional version of the classical Knaster, Kuratowski and Mazurkiewicz Lemma (KKM Lemma) in 1961. Studied are applications of general system versions of minimax inequalities and generalized quasi-variational inequalities, and random abstract economies and its applications to the system of random quasi-variational inequalities are given.

Optimization: Techniques And Applications (Icota '95)

Optimization: Techniques And Applications (Icota '95) PDF

Author: G Z Liu

Publisher: World Scientific

Published: 1995-09-01

Total Pages: 1718

ISBN-13: 9814549150

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With the advent of powerful computers and novel mathematical programming techniques, the multidisciplinary field of optimization has advanced to the stage that quite complicated systems can be addressed. The conference was organized to provide a platform for the exchange of new ideas and information and for identifying needs for future research. The contributions covered both theoretical techniques and a rich variety of case studies to which optimization can be usefully applied.

Variational Methods in Partially Ordered Spaces

Variational Methods in Partially Ordered Spaces PDF

Author: Alfred Göpfert

Publisher: Springer Science & Business Media

Published: 2006-04-18

Total Pages: 359

ISBN-13: 0387217436

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This book discusses basic tools of partially ordered spaces and applies them to variational methods in Nonlinear Analysis and for optimizing problems. This book is aimed at graduate students and research mathematicians.

Vector Variational Inequalities and Vector Optimization

Vector Variational Inequalities and Vector Optimization PDF

Author: Qamrul Hasan Ansari

Publisher: Springer

Published: 2017-10-31

Total Pages: 509

ISBN-13: 3319630490

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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.

Vector Variational Inequalities and Vector Equilibria

Vector Variational Inequalities and Vector Equilibria PDF

Author: F. Giannessi

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 522

ISBN-13: 1461302994

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The book deals with the mathematical theory of vector variational inequalities with special reference to equilibrium problems. Such models have been introduced recently to study new problems from mechanics, structural engineering, networks, and industrial management, and to revisit old ones. The common feature of these problems is that given by the presence of concurrent objectives and by the difficulty of identifying a global functional (like energy) to be extremized. The vector variational inequalities have the advantage of both the variational ones and vector optimization which are found as special cases. Among several applications, the equilibrium flows on a network receive special attention. Audience: The book is addressed to academic researchers as well as industrial ones, in the fields of mathematics, engineering, mathematical programming, control theory, operations research, computer science, and economics.

Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem

Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem PDF

Author: Lawrence C. Evans

Publisher: American Mathematical Soc.

Published: 1999

Total Pages: 66

ISBN-13: 0821809385

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In this volume, the authors demonstrate under some assumptions on $f^+$, $f^-$ that a solution to the classical Monge-Kantorovich problem of optimally rearranging the measure $\mu{^+}=f^+dx$ onto $\mu^-=f^-dy$ can be constructed by studying the $p$-Laplacian equation $- \mathrm{div}(\vert DU_p\vert^{p-2}Du_p)=f^+-f^-$ in the limit as $p\rightarrow\infty$. The idea is to show $u_p\rightarrow u$, where $u$ satisfies $\vert Du\vert\leq 1,-\mathrm{div}(aDu)=f^+-f^-$ for some density $a\geq0$, and then to build a flow by solving a nonautonomous ODE involving $a, Du, f^+$ and $f^-$.

The Riemann Problem for the Transportation Equations in Gas Dynamics

The Riemann Problem for the Transportation Equations in Gas Dynamics PDF

Author: Wancheng Sheng

Publisher: American Mathematical Soc.

Published: 1999

Total Pages: 77

ISBN-13: 0821809474

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In this volume, the one-dimensional and two-dimensional Riemann problems for the transportation equations in gas dynamics are solved constructively. In either the 1-D or 2-D case, there are only two kinds of solutions: one involves Dirac delta waves, and the other involves vacuums, which have been merely discussed so far. The generalized Rankine-Hugoniot and entropy conditions for Dirac delta waves are clarified with viscous vanishing method. All of the existence, uniqueness and stability for viscous perturbations are proved analytically.

Abelian Galois Cohomology of Reductive Groups

Abelian Galois Cohomology of Reductive Groups PDF

Author: Mikhail Borovoi

Publisher: American Mathematical Soc.

Published: 1998

Total Pages: 50

ISBN-13: 0821806505

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In this volume, a new functor $H^2_{ab}(K,G)$ of abelian Galois cohomology is introduced from the category of connected reductive groups $G$ over a field $K$ of characteristic $0$ to the category of abelian groups. The abelian Galois cohomology and the abelianization map$ab^1:H^1(K,G) \rightarrow H^2_{ab}(K,G)$ are used to give a functorial, almost explicit description of the usual Galois cohomology set $H^1(K,G)$ when $K$ is a number field.

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