On The Efficient Solution Of Variational Inequalities

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Differential and Integral Inequalities

Author : Dorin Andrica
Publisher : Springer Nature
ISBN 13 : 3030274071
Total Pages : 848 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Differential and Integral Inequalities by : Dorin Andrica

Download or read book Differential and Integral Inequalities written by Dorin Andrica and published by Springer Nature. This book was released on 2019-11-14 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theories, methods and problems in approximation theory and analytic inequalities with a focus on differential and integral inequalities are analyzed in this book. Fundamental and recent developments are presented on the inequalities of Abel, Agarwal, Beckenbach, Bessel, Cauchy–Hadamard, Chebychev, Markov, Euler’s constant, Grothendieck, Hilbert, Hardy, Carleman, Landau–Kolmogorov, Carlson, Bernstein–Mordell, Gronwall, Wirtinger, as well as inequalities of functions with their integrals and derivatives. Each inequality is discussed with proven results, examples and various applications. Graduate students and advanced research scientists in mathematical analysis will find this reference essential to their understanding of differential and integral inequalities. Engineers, economists, and physicists will find the highly applicable inequalities practical and useful to their research.

Network Economics

Author : Anna Nagurney
Publisher : Springer Science & Business Media
ISBN 13 : 1475730055
Total Pages : 423 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Network Economics by : Anna Nagurney

Download or read book Network Economics written by Anna Nagurney and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces

Author : Michael Ulbrich
Publisher : SIAM
ISBN 13 : 1611970687
Total Pages : 315 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces by : Michael Ulbrich

Download or read book Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces written by Michael Ulbrich and published by SIAM. This book was released on 2011-07-28 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Continuous Optimization and Variational Inequalities

Author : Anurag Jayswal
Publisher : CRC Press
ISBN 13 : 1000648931
Total Pages : 379 pages
Book Rating : 4.0/5 (6 download)

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Book Synopsis Continuous Optimization and Variational Inequalities by : Anurag Jayswal

Download or read book Continuous Optimization and Variational Inequalities written by Anurag Jayswal and published by CRC Press. This book was released on 2022-09-13 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proposed book provides a comprehensive coverage of theory and methods in the areas of continuous optimization and variational inequality. It describes theory and solution methods for optimization with smooth and non-smooth functions, for variational inequalities with single-valued and multivalued mappings, and for related classes such as mixed variational inequalities, complementarity problems, and general equilibrium problems. The emphasis is made on revealing generic properties of these problems that allow creation of efficient solution methods. Salient Features The book presents a deep, wide-ranging introduction to the theory of the optimal control of processes governed by optimization techniques and variational inequality Several solution methods are provided which will help the reader to develop various optimization tools for real-life problems which can be modeled by optimization techniques involving linear and nonlinear functions. The book focuses on most recent contributions in the nonlinear phenomena, which can appear in various areas of human activities. This book also presents relevant mathematics clearly and simply to help solve real life problems in diverse fields such as mechanical engineering, management, control behavior, traffic signal, industry, etc. This book is aimed primarily at advanced undergraduates and graduate students pursuing computer engineering and electrical engineering courses. Researchers, academicians and industry people will also find this book useful.

Vector Variational Inequalities and Vector Optimization

Author : Qamrul Hasan Ansari
Publisher : Springer
ISBN 13 : 3319630490
Total Pages : 517 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Vector Variational Inequalities and Vector Optimization by : Qamrul Hasan Ansari

Download or read book Vector Variational Inequalities and Vector Optimization written by Qamrul Hasan Ansari and published by Springer. This book was released on 2017-10-31 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Quadratic Programming and Affine Variational Inequalities

Author : Gue Myung Lee
Publisher : Springer Science & Business Media
ISBN 13 : 0387242783
Total Pages : 353 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Quadratic Programming and Affine Variational Inequalities by : Gue Myung Lee

Download or read book Quadratic Programming and Affine Variational Inequalities written by Gue Myung Lee and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quadratic programs and affine variational inequalities represent two fundamental, closely-related classes of problems in the t,heories of mathematical programming and variational inequalities, resp- tively. This book develops a unified theory on qualitative aspects of nonconvex quadratic programming and affine variational inequ- ities. The first seven chapters introduce the reader step-by-step to the central issues concerning a quadratic program or an affine variational inequality, such as the solution existence, necessary and sufficient conditions for a point to belong to the solution set, and properties of the solution set. The subsequent two chapters discuss briefly two concrete nlodels (linear fractional vector optimization and the traffic equilibrium problem) whose analysis can benefit a lot from using the results on quadratic programs and affine variational inequalities. There are six chapters devoted to the study of conti- ity and/or differentiability properties of the characteristic maps and functions in quadratic programs and in affine variational inequa- ties where all the components of the problem data are subject to perturbation. Quadratic programs and affine variational inequa- ties under linear perturbations are studied in three other chapters. One special feature of the presentation is that when a certain pr- erty of a characteristic map or function is investigated, we always try first to establish necessary conditions for it to hold, then we go on to study whether the obtained necessary conditions are suf- cient ones. This helps to clarify the structures of the two classes of problems under consideration.

Optimization, Variational Analysis and Applications

Author : Vivek Laha
Publisher : Springer Nature
ISBN 13 : 9811618194
Total Pages : 441 pages
Book Rating : 4.8/5 (116 download)

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Book Synopsis Optimization, Variational Analysis and Applications by : Vivek Laha

Download or read book Optimization, Variational Analysis and Applications written by Vivek Laha and published by Springer Nature. This book was released on 2021-07-27 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes selected papers presented at the Indo-French Seminar on Optimization, Variational Analysis and Applications (IFSOVAA-2020), held at the Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India, from 2–4 February 2020. The book discusses current optimization problems and their solutions by using the powerful tool of variational analysis. Topics covered in this volume include set optimization, multiobjective optimization, mathematical programs with complementary, equilibrium, vanishing and switching constraints, copositive optimization, interval-valued optimization, sequential quadratic programming, bound-constrained optimization, variational inequalities, and more. Several applications in different branches of applied mathematics, engineering, economics, finance, and medical sciences have been included. Each chapter not only provides a detailed survey of the topic but also builds systematic theories and suitable algorithms to deduce the most recent findings in literature. This volume appeals to graduate students as well as researchers and practitioners in pure and applied mathematics and related fields that make use of variational analysis in solving optimization problems.

Vector Variational Inequalities and Vector Equilibria

Author : F. Giannessi
Publisher : Springer Science & Business Media
ISBN 13 : 1461302994
Total Pages : 522 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Vector Variational Inequalities and Vector Equilibria by : F. Giannessi

Download or read book Vector Variational Inequalities and Vector Equilibria written by F. Giannessi and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2013 Edition

Author :
Publisher : ScholarlyEditions
ISBN 13 : 1490106189
Total Pages : 772 pages
Book Rating : 4.4/5 (91 download)

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Book Synopsis Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2013 Edition by :

Download or read book Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 772 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Mathematical Analysis. The editors have built Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Mathematical Analysis in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Calculus, Mathematical Analysis, and Nonlinear Research: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Optimality Conditions in Vector Optimization

Author : Manuel Arana Jiménez
Publisher : Bentham Science Publishers
ISBN 13 : 1608051102
Total Pages : 194 pages
Book Rating : 4.6/5 (8 download)

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Book Synopsis Optimality Conditions in Vector Optimization by : Manuel Arana Jiménez

Download or read book Optimality Conditions in Vector Optimization written by Manuel Arana Jiménez and published by Bentham Science Publishers. This book was released on 2010 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vector optimization is continuously needed in several science fields, particularly in economy, business, engineering, physics and mathematics. The evolution of these fields depends, in part, on the improvements in vector optimization in mathematical programming. The aim of this Ebook is to present the latest developments in vector optimization. The contributions have been written by some of the most eminent researchers in this field of mathematical programming. The Ebook is considered essential for researchers and students in this field.

Complementarity, Equilibrium, Efficiency and Economics

Author : G. Isac
Publisher : Springer Science & Business Media
ISBN 13 : 1475736231
Total Pages : 458 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Complementarity, Equilibrium, Efficiency and Economics by : G. Isac

Download or read book Complementarity, Equilibrium, Efficiency and Economics written by G. Isac and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: In complementarity theory, which is a relatively new domain of applied mathematics, several kinds of mathematical models and problems related to the study of equilibrium are considered from the point of view of physics as well as economics. In this book the authors have combined complementarity theory, equilibrium of economical systems, and efficiency in Pareto's sense. The authors discuss the use of complementarity theory in the study of equilibrium of economic systems and present results they have obtained. In addition the authors present several new results in complementarity theory and several numerical methods for solving complementarity problems associated with the study of economic equilibrium. The most important notions of Pareto efficiency are also presented. Audience: Researchers and graduate students interested in complementarity theory, in economics, in optimization, and in applied mathematics.

Variational Inequalities and Network Equilibrium Problems

Author : F. Giannessi
Publisher : Springer Science & Business Media
ISBN 13 : 1489913580
Total Pages : 304 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis Variational Inequalities and Network Equilibrium Problems by : F. Giannessi

Download or read book Variational Inequalities and Network Equilibrium Problems written by F. Giannessi and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings forth a set of papers presented at the conference on "Varia tional Inequalities and network equilibrium problems", held in Erice at the "G. Stam pacchia" School of the "E. Majorana" Centre for Scientific Culture in the period 19~25 June 1994. The meeting was conceived to contribute to the exchange between Variational Analysis and equilibrium problems, especially those related to network design. Most of the approaches and viewpoints of these fields are present in the volume, both as concerns the theory and the applications of equilibrium problems to transportation, computer and electric networks, to market behavior, and to bi~level programming. Being convinced of the great importance of equilibrium problems as well as of their complexity, the organizers hope that the merging of points of view coming from differ ent fields will stimulate theoretical research and applications. In this context Variational and Quasi~Variational Inequalities have shown them selves to be very important models for equilibrium problems. As a consequence in the last two decades they have received a lot of attention both as to mathematical inves tigation and applications. The proof that the above mentioned equilibrium problems can be expressed, in terms of Variational or Quasi~Variational Inequalities also in the non~standard and non~symmetric cases, has been a crucial improvement.

Generalized Convexity and Vector Optimization

Author : Shashi K. Mishra
Publisher : Springer Science & Business Media
ISBN 13 : 3540856714
Total Pages : 298 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Generalized Convexity and Vector Optimization by : Shashi K. Mishra

Download or read book Generalized Convexity and Vector Optimization written by Shashi K. Mishra and published by Springer Science & Business Media. This book was released on 2008-12-19 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present lecture note is dedicated to the study of the optimality conditions and the duality results for nonlinear vector optimization problems, in ?nite and in?nite dimensions. The problems include are nonlinear vector optimization problems, s- metric dual problems, continuous-time vector optimization problems, relationships between vector optimization and variational inequality problems. Nonlinear vector optimization problems arise in several contexts such as in the building and interpretation of economic models; the study of various technolo- cal processes; the development of optimal choices in ?nance; management science; production processes; transportation problems and statistical decisions, etc. In preparing this lecture note a special effort has been made to obtain a se- contained treatment of the subjects; so we hope that this may be a suitable source for a beginner in this fast growing area of research, a semester graduate course in nonlinear programing, and a good reference book. This book may be useful to theoretical economists, engineers, and applied researchers involved in this area of active research. The lecture note is divided into eight chapters: Chapter 1 brie?y deals with the notion of nonlinear programing problems with basic notations and preliminaries. Chapter 2 deals with various concepts of convex sets, convex functions, invex set, invex functions, quasiinvex functions, pseudoinvex functions, type I and generalized type I functions, V-invex functions, and univex functions.

Nonlinear Analysis: Problems, Applications and Computational Methods

Author : Zakia Hammouch
Publisher : Springer Nature
ISBN 13 : 3030622991
Total Pages : 249 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Nonlinear Analysis: Problems, Applications and Computational Methods by : Zakia Hammouch

Download or read book Nonlinear Analysis: Problems, Applications and Computational Methods written by Zakia Hammouch and published by Springer Nature. This book was released on 2020-11-13 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of original research papers as proceedings of the 6th International Congress of the Moroccan Society of Applied Mathematics organized by Sultan Moulay Slimane University, Morocco, during 7th–9th November 2019. It focuses on new problems, applications and computational methods in the field of nonlinear analysis. It includes various topics including fractional differential systems of various types, time-fractional systems, nonlinear Jerk equations, reproducing kernel Hilbert space method, thrombin receptor activation mechanism model, labour force evolution model, nonsmooth vector optimization problems, anisotropic elliptic nonlinear problem, viscous primitive equations of geophysics, quadratic optimal control problem, multi-orthogonal projections and generalized continued fractions. The conference aimed at fostering cooperation among students, researchers and experts from diverse areas of applied mathematics and related sciences through fruitful deliberations on new research findings. This book is expected to be resourceful for researchers, educators and graduate students interested in applied mathematics and interactions of mathematics with other branches of science and engineering.

Numerical Analysis and Optimization

Author : Mehiddin Al-Baali
Publisher : Springer
ISBN 13 : 3319176897
Total Pages : 351 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Numerical Analysis and Optimization by : Mehiddin Al-Baali

Download or read book Numerical Analysis and Optimization written by Mehiddin Al-Baali and published by Springer. This book was released on 2015-07-16 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the latest findings in the field of numerical analysis and optimization, this volume balances pure research with practical applications of the subject. Accompanied by detailed tables, figures, and examinations of useful software tools, this volume will equip the reader to perform detailed and layered analysis of complex datasets. Many real-world complex problems can be formulated as optimization tasks. Such problems can be characterized as large scale, unconstrained, constrained, non-convex, non-differentiable, and discontinuous, and therefore require adequate computational methods, algorithms, and software tools. These same tools are often employed by researchers working in current IT hot topics such as big data, optimization and other complex numerical algorithms on the cloud, devising special techniques for supercomputing systems. The list of topics covered include, but are not limited to: numerical analysis, numerical optimization, numerical linear algebra, numerical differential equations, optimal control, approximation theory, applied mathematics, algorithms and software developments, derivative free optimization methods and programming models. The volume also examines challenging applications to various types of computational optimization methods which usually occur in statistics, econometrics, finance, physics, medicine, biology, engineering and industrial sciences.

Generalized Convexity, Generalized Monotonicity and Applications

Author : Andrew Eberhard
Publisher : Springer Science & Business Media
ISBN 13 : 0387236392
Total Pages : 342 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Generalized Convexity, Generalized Monotonicity and Applications by : Andrew Eberhard

Download or read book Generalized Convexity, Generalized Monotonicity and Applications written by Andrew Eberhard and published by Springer Science & Business Media. This book was released on 2006-06-22 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there is a growing interest in generalized convex fu- tions and generalized monotone mappings among the researchers of - plied mathematics and other sciences. This is due to the fact that mathematical models with these functions are more suitable to describe problems of the real world than models using conventional convex and monotone functions. Generalized convexity and monotonicity are now considered as an independent branch of applied mathematics with a wide range of applications in mechanics, economics, engineering, finance and many others. The present volume contains 20 full length papers which reflect c- rent theoretical studies of generalized convexity and monotonicity, and numerous applications in optimization, variational inequalities, equil- rium problems etc. All these papers were refereed and carefully selected from invited talks and contributed talks that were presented at the 7th International Symposium on Generalized Convexity/Monotonicity held in Hanoi, Vietnam, August 27-31, 2002. This series of Symposia is or- nized by the Working Group on Generalized Convexity (WGGC) every 3 years and aims to promote and disseminate research on the field. The WGGC (http://www.genconv.org) consists of more than 300 researchers coming from 36 countries.

Numerical Methods for Nonlinear Variational Problems

Author : Roland Glowinski
Publisher : Springer
ISBN 13 : 9783662126158
Total Pages : 493 pages
Book Rating : 4.1/5 (261 download)

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Book Synopsis Numerical Methods for Nonlinear Variational Problems by : Roland Glowinski

Download or read book Numerical Methods for Nonlinear Variational Problems written by Roland Glowinski and published by Springer. This book was released on 2013-10-03 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the mathematical background and reviews the techniques for solving problems, including those that require large computations such as transonic flows for compressible fluids and the Navier-Stokes equations for incompressible viscous fluids. Finite element approximations and non-linear relaxation, and nonlinear least square methods are all covered in detail, as are many applications. This volume is a classic in a long-awaited softcover re-edition.