Download or read book Nonlinear Programming and Variational Inequality Problems written by Michael Patriksson and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Equilibrium Problems Nonsmooth Optimization and Variational Inequality Models written by F. Giannessi and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Download or read book Nonlinear Programming and Variational Inequalities written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Cones and Functions in Optimization and Variational Inequalities written by Alfred Auslender and published by Springer Science & Business Media. This book was released on 2006-05-07 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This systematic and comprehensive account of asymptotic sets and functions develops a broad and useful theory in the areas of optimization and variational inequalities. The central focus is on problems of handling unbounded situations, using solutions of a given problem in these classes, when for example standard compacity hypothesis is not present. This book will interest advanced graduate students, researchers, and practitioners of optimization theory, nonlinear programming, and applied mathematics.
Download or read book Nonlinear Optimization and Applications written by Gianni Pillo and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Nonlinear Programming Variational Inequalities and Stochastic Programming written by and published by . This book was released on 2009 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Optimization and Related Topics written by Gianni Pillo and published by Springer Science & Business Media. This book was released on 2000-04-30 with total page 854 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 309 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.
Download or read book Finite Dimensional Variational Inequalities and Complementarity Problems written by Francisco Facchinei and published by Springer Science & Business Media. This book was released on 2007-06-14 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Nonlinear Programming Techniques for Equilibria written by Giancarlo Bigi and published by Springer. This book was released on 2018-09-20 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Download or read book Generalized Convexity Nonsmooth Variational Inequalities and Nonsmooth Optimization written by Qamrul Hasan Ansari and published by CRC Press. This book was released on 2013-07-18 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Until now, no book addressed convexity, monotonicity, and variational inequalities together. Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization covers all three topics, including new variational inequality problems defined by a bifunction.The first part of the book focuses on generalized convexity and generalized
Download or read book Optimal Quadratic Programming Algorithms written by Zdenek Dostál and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Asymptotic Cones and Functions in Optimization and Variational Inequalities written by Alfred Auslender and published by Springer. This book was released on 2013-04-10 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: This systematic and comprehensive account of asymptotic sets and functions develops a broad and useful theory in the areas of optimization and variational inequalities. The central focus is on problems of handling unbounded situations, using solutions of a given problem in these classes, when for example standard compacity hypothesis is not present. This book will interest advanced graduate students, researchers, and practitioners of optimization theory, nonlinear programming, and applied mathematics.
Download or read book International Conference on Nonlinear Programming and Variational Inequalities written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advances in Nonlinear Programming written by Ya-xiang Yuan and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: About 60 scientists and students attended the 96' International Conference on Nonlinear Programming, which was held September 2-5 at Institute of Compu tational Mathematics and Scientific/Engineering Computing (ICMSEC), Chi nese Academy of Sciences, Beijing, China. 25 participants were from outside China and 35 from China. The conference was to celebrate the 60's birthday of Professor M.J.D. Powell (Fellow of Royal Society, University of Cambridge) for his many contributions to nonlinear optimization. On behalf of the Chinese Academy of Sciences, vice president Professor Zhi hong Xu attended the opening ceremony of the conference to express his warm welcome to all the participants. After the opening ceremony, Professor M.J.D. Powell gave the keynote lecture "The use of band matrices for second derivative approximations in trust region methods". 13 other invited lectures on recent advances of nonlinear programming were given during the four day meeting: "Primal-dual methods for nonconvex optimization" by M. H. Wright (SIAM President, Bell Labs), "Interior point trajectories in semidefinite programming" by D. Goldfarb (Columbia University, Editor-in-Chief for Series A of Mathe matical Programming), "An approach to derivative free optimization" by A.
