Nonlinear Programming And Variational Inequality Problems

Author : Michael Patriksson
Publisher : Springer Science & Business Media
Page : 343 pages
File Size : 53,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475729917

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Nonlinear Programming and Variational Inequality Problems by Michael Patriksson Pdf

Since I started working in the area of nonlinear programming and, later on, variational inequality problems, I have frequently been surprised to find that many algorithms, however scattered in numerous journals, monographs and books, and described rather differently, are closely related to each other. This book is meant to help the reader understand and relate algorithms to each other in some intuitive fashion, and represents, in this respect, a consolidation of the field. The framework of algorithms presented in this book is called Cost Approxi mation. (The preface of the Ph.D. thesis [Pat93d] explains the background to the work that lead to the thesis, and ultimately to this book.) It describes, for a given formulation of a variational inequality or nonlinear programming problem, an algorithm by means of approximating mappings and problems, a principle for the update of the iteration points, and a merit function which guides and monitors the convergence of the algorithm. One purpose of this book is to offer this framework as an intuitively appeal ing tool for describing an algorithm. One of the advantages of the framework, or any reasonable framework for that matter, is that two algorithms may be easily related and compared through its use. This framework is particular in that it covers a vast number of methods, while still being fairly detailed; the level of abstraction is in fact the same as that of the original problem statement.

Author : F. Giannessi,A. Maugeri,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 55,9 Mb
Release : 2006-04-11
Category : Mathematics
ISBN : 9780306480263

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Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models by F. Giannessi,A. Maugeri,Panos M. Pardalos Pdf

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 : Gue Myung Lee,N.N. Tam,Nguyen Dong Yen
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 54,7 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9780387242781

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Quadratic Programming and Affine Variational Inequalities by Gue Myung Lee,N.N. Tam,Nguyen Dong Yen Pdf

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.

Author : Gianni Pillo,F. Giannessi
Publisher : Springer Science & Business Media
Page : 484 pages
File Size : 42,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475732269

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Nonlinear Optimization and Related Topics by Gianni Pillo,F. Giannessi Pdf

This volume contains the edited texts of the lectures presented at the Workshop on Nonlinear Optimization held in Erice, Sicily, at the "G. Stampacchia" School of Mathematics of the "E. Majorana" Centre for Scientific Culture, June 23 -July 2, 1998. In the tradition of these meetings, the main purpose was to review and discuss recent advances and promising research trends concerning theory, algorithms and innovative applications in the field of Nonlinear Optimization, and of related topics such as Convex Optimization, Nonsmooth Optimization, Variational Inequalities and Complementarity Problems. The meeting was attended by 83 people from 21 countries. Besides the lectures, several formal and informal discussions took place. The result was a wide and deep knowledge of the present research tendencies in the field. We wish to express our appreciation for the active contribution of all the par ticipants in the meeting. Our gratitude is due to the Ettore Majorana Centre in Erice, which offered its facilities and rewarding environment: its staff was certainly instrumental for the success of the meeting. Our gratitude is also due to Francisco Facchinei and Massimo Roma for the effort and time devoted as members of the Organising Committee. We are indebted to the Italian National Research Council, and in particular to the Group on Functional Analysis and its Applications and to the Committees on Engineering Sciences and on Information Sciences and Technolo gies for their financial support. Finally, we address our thanks to Kluwer Academic Publishers for having offered to publish this volume.

Author : Gianni Pillo,F. Giannessi
Publisher : Springer Science & Business Media
Page : 367 pages
File Size : 51,5 Mb
Release : 2013-11-11
Category : Computers
ISBN : 9781489902894

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Nonlinear Optimization and Applications by Gianni Pillo,F. Giannessi Pdf

This volume contains the edited texts of the lectures presented at the workshop on Nonlinear Optimization: Theory and Applications, held in Erice at the "G. Stampacchia" School of Mathematics of the "E. Majorana" International Centre for Scientific Culture June 13-21, 1995. The meeting was conceived to review and discuss recent advances and promising research trends concerning theory, algorithms, and innovative applications in the field This is a field of mathematics which is providing viable of Nonlinear Optimization. tools in engineering, in economics and in other applied sciences, and which is giving a great contribution also in the solution of the more practiced linear optimization prob lems. The meeting was attended by approximately 70 people from 18 countries. Besides the lectures, several formal and informal discussions took place. The result was a broad exposure providing a wide and deep understanding of the present research achievements in the field. We wish to express our appreciation for the active contributions of all the partici pants in the meeting. Our gratitude is due to the Ettore Majorana Center in Erice, which offered its facilities and stimulating environment: its staff was certainly instrumental for the success of the meeting. Our gratitude is also due to Francisco Facchinei and Massino Roma for the time spent in the organization of the workshop, and to Giuliana Cai for the careful typesetting of this volume.

Author : F. Giannessi,A. Maugeri
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 48,8 Mb
Release : 2013-06-29
Category : Social Science
ISBN : 9781489913586

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Variational Inequalities and Network Equilibrium Problems by F. Giannessi,A. Maugeri Pdf

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.

Author : Anurag Jayswal,Tadeusz Antczak
Publisher : CRC Press
Page : 309 pages
File Size : 53,9 Mb
Release : 2022-09-13
Category : Technology & Engineering
ISBN : 9781000648980

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Continuous Optimization and Variational Inequalities by Anurag Jayswal,Tadeusz Antczak Pdf

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.

Author : Giancarlo Bigi,Marco Castellani,Massimo Pappalardo,Mauro Passacantando
Publisher : Springer
Page : 120 pages
File Size : 45,6 Mb
Release : 2018-09-20
Category : Business & Economics
ISBN : 9783030002053

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Nonlinear Programming Techniques for Equilibria by Giancarlo Bigi,Marco Castellani,Massimo Pappalardo,Mauro Passacantando Pdf

This book considers a range of problems in operations research, which are formulated through various mathematical models such as complementarity, variational inequalities, multiobjective optimization, fixed point problems, noncooperative games and inverse optimization. Moreover, the book subsumes all these models under a common structure that allows them to be formulated in a unique format: the Ky Fan inequality. It subsequently focuses on this unifying equilibrium format, providing a comprehensive overview of the main theoretical results and solution algorithms, together with a wealth of applications and numerical examples. Particular emphasis is placed on the role of nonlinear optimization techniques – e.g. convex optimization, nonsmooth calculus, proximal point and descent algorithms – as valuable tools for analyzing and solving Ky Fan inequalities.

Author : Francisco Facchinei,Jong-Shi Pang
Publisher : Springer Science & Business Media
Page : 693 pages
File Size : 55,9 Mb
Release : 2007-06-14
Category : Mathematics
ISBN : 9780387218144

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Finite-Dimensional Variational Inequalities and Complementarity Problems by Francisco Facchinei,Jong-Shi Pang Pdf

This is part one of a two-volume work presenting a comprehensive treatment of the finite-dimensional variational inequality and complementarity problem. It covers the basic theory of 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.

Author : Olvi L. Mangasarian,Robert R. Meyer,Stephen M. Robinson
Publisher : Unknown
Page : 504 pages
File Size : 41,8 Mb
Release : 1978
Category : Mathematics
ISBN : UOM:39015006369832

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Nonlinear Programming 3 by Olvi L. Mangasarian,Robert R. Meyer,Stephen M. Robinson Pdf

Author : Huey-Kuo Chen
Publisher : Springer Science & Business Media
Page : 328 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642599804

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Dynamic Travel Choice Models by Huey-Kuo Chen Pdf

Contains up-to-date and accessible material, plus all the necessary mathematical background. By verifying the asymmetric property of the dynamic link travel time function, while identifying the inflow, exit flow and number of vehicles on a physical link as three different states over time, the author adopts a variational inequality approach using one time-space link variable. This is then used to formulate problems with deterministic, stochastic and fuzzy traffic information. The book is thus of particular interest to those readers involved in aspects of model formulation, solution algorithm, equivalence analysis and numerical examples.

Author : Francisco Facchinei,Jong-Shi Pang
Publisher : Springer Science & Business Media
Page : 698 pages
File Size : 46,6 Mb
Release : 2007-06-04
Category : Business & Economics
ISBN : 9780387218151

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Finite-Dimensional Variational Inequalities and Complementarity Problems by Francisco Facchinei,Jong-Shi Pang Pdf

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.

Author : Zdenek Dostál
Publisher : Springer
Page : 0 pages
File Size : 55,8 Mb
Release : 2008-11-01
Category : Mathematics
ISBN : 0387571442

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Optimal Quadratic Programming Algorithms by Zdenek Dostál Pdf

Quadratic programming (QP) is one advanced mathematical technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. This book presents recently developed algorithms for solving large QP problems and focuses on algorithms which are, in a sense optimal, i.e., they can solve important classes of problems at a cost proportional to the number of unknowns. For each algorithm presented, the book details its classical predecessor, describes its drawbacks, introduces modifications that improve its performance, and demonstrates these improvements through numerical experiments. This self-contained monograph can serve as an introductory text on quadratic programming for graduate students and researchers. Additionally, since the solution of many nonlinear problems can be reduced to the solution of a sequence of QP problems, it can also be used as a convenient introduction to nonlinear programming.

Author : C.j. Goh
Publisher : Taylor & Francis
Page : 344 pages
File Size : 51,6 Mb
Release : 2002-05-10
Category : Mathematics
ISBN : 0415274796

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Duality in Optimization and Variational Inequalities by C.j. Goh Pdf

This comprehensive volume covers a wide range of duality topics ranging from simple ideas in network flows to complex issues in non-convex optimization and multicriteria problems. In addition, it examines duality in the context of variational inequalities and vector variational inequalities, as generalizations to optimization. Duality in Optimization and Variational Inequalities is intended for researchers and practitioners of optimization with the aim of enhancing their understanding of duality. It provides a wider appreciation of optimality conditions in various scenarios and under different assumptions. It will enable the reader to use duality to devise more effective computational methods, and to aid more meaningful interpretation of optimization and variational inequality problems.

Author : Michael C. Ferris,Jong-Shi Pang
Publisher : SIAM
Page : 494 pages
File Size : 53,7 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 0898713919

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Complementarity and Variational Problems by Michael C. Ferris,Jong-Shi Pang Pdf

After more than three decades of research, the subject of complementarity problems and its numerous extensions has become a well-established and fruitful discipline within mathematical programming and applied mathematics. Sources of these problems are diverse and span numerous areas in engineering, economics, and the sciences. Includes refereed articles.