Download or read book Algorithms for Complementarity Problems and Generalized Equations written by Stephen Clyde Billups and published by . This book was released on 1995 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Encyclopedia of Optimization written by Christodoulos A. Floudas and published by Springer Science & Business Media. This book was released on 2008-09-04 with total page 4646 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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".
Download or read book A Unified Approach to Interior Point Algorithms for Linear Complementarity Problems written by Masakazu Kojima and published by Springer Science & Business Media. This book was released on 1991-09-25 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following Karmarkar's 1984 linear programming algorithm, numerous interior-point algorithms have been proposed for various mathematical programming problems such as linear programming, convex quadratic programming and convex programming in general. This monograph presents a study of interior-point algorithms for the linear complementarity problem (LCP) which is known as a mathematical model for primal-dual pairs of linear programs and convex quadratic programs. A large family of potential reduction algorithms is presented in a unified way for the class of LCPs where the underlying matrix has nonnegative principal minors (P0-matrix). This class includes various important subclasses such as positive semi-definite matrices, P-matrices, P*-matrices introduced in this monograph, and column sufficient matrices. The family contains not only the usual potential reduction algorithms but also path following algorithms and a damped Newton method for the LCP. The main topics are global convergence, global linear convergence, and the polynomial-time convergence of potential reduction algorithms included in the family.
Download or read book Algorithms and Interfaces for Structured Variational Inequalities and Their Extensions written by Youngdae Kim and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Variational inequalities (VIs) are a generalization of nonlinear system of equations, so-called generalized equations. In addition to the system of equations, they subsume geometric first-order optimality conditions, nonlinear (linear) complementarity problems, and mixed complementarity problems. Representative applications are equilibrium problems such as generalized Nash equilibrium problems (GNEPs) and multiple optimization problems with equilibrium constraints (MOPECs). This thesis is concerned with algorithms and interfaces for structured variational inequalities and their extensions. Algorithms and interfaces are closely related to each other in a way that interfaces helping identify problem structures can lead to more robust and efficient algorithms, and structure-exploiting algorithms can guide us to design better structure-exposing interfaces. Interfaces exposing problem structures are described based on an extended mathematical programming (EMP) framework, where the framework allows us to formulate equilibrium problems in a natural and intuitive way in modeling languages, for example AMPL, GAMS, or Julia, without requiring the modeler to supply derivatives. Extensions to support some complicated structures such as shared constraints, shared variables, and quasi-variational inequalities (QVIs) are presented. Our interfaces generate a human-readable file from which we can easily identify high-level structure of the problem. We present an extension to PATH and two general-purpose solvers, PATHAVI and SELKIE, each of which utilizes problem structures, such as implicitly defined variables, polyhedral constraints, and groups of interacting agents, respectively. These structures are identified through our interfaces. An extension to PATH exploits implicitly defined variables by restoring their feasibility via projection using the implicit function theorem. Projection is performed in both their primal and dual spaces. PATHAVI is a structure-preserving solver for affine variational inequalities such that it follows a piecewise-linear (PL) path on a PL-manifold constructed using given polyhedral constraints without applying any reduction. This is a key contrast to the existing solver PATH which is oblivious of those constraints except for preprocessing purposes and a QR decomposition-based method that performs a reduction, thus destroying the structure, if there is nontrivial lineality space. SELKIE is a solver for equilibrium problems which enables various decomposition schemes based on groups of agents information to be instantiated in a flexible and adaptable way. Parallelism can be achieved either whenever independent groups of agents are detected or per user's request. A sub-solver for each sub-model can be chosen so that a highly efficient solver can be employed tailored to a certain problem type. Examples illustrating the efficiency and effectiveness of our extension and solvers are given. All our interfaces and solvers have been implemented and are available within GAMS/EMP.
Download or read book Complementarity Applications Algorithms and Extensions written by Michael C. Ferris and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents state-of-the-art complementarity applications, algorithms, extensions and theory in the form of eighteen papers. These at the International Conference on Com invited papers were presented plementarity 99 (ICCP99) held in Madison, Wisconsin during June 9-12, 1999 with support from the National Science Foundation under Grant DMS-9970102. Complementarity is becoming more widely used in a variety of appli cation areas. In this volume, there are papers studying the impact of complementarity in such diverse fields as deregulation of electricity mar kets, engineering mechanics, optimal control and asset pricing. Further more, application of complementarity and optimization ideas to related problems in the burgeoning fields of machine learning and data mining are also covered in a series of three articles. In order to effectively process the complementarity problems that arise in such applications, various algorithmic, theoretical and computational extensions are covered in this volume. Nonsmooth analysis has an im portant role to play in this area as can be seen from articles using these tools to develop Newton and path following methods for constrained nonlinear systems and complementarity problems. Convergence issues are covered in the context of active set methods, global algorithms for pseudomonotone variational inequalities, successive convex relaxation and proximal point algorithms. Theoretical contributions to the connectedness of solution sets and constraint qualifications in the growing area of mathematical programs with equilibrium constraints are also presented. A relaxation approach is given for solving such problems. Finally, computational issues related to preprocessing mixed complementarity problems are addressed.
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 2007-06-04 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Nonsmooth Approach to Optimization Problems with Equilibrium Constraints written by Jiri Outrata and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Complementarity and Variational Problems written by Michael C. Ferris and published by SIAM. This book was released on 1997-01-01 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Frontiers in Applied General Equilibrium Modeling written by Timothy J. Kehoe and published by Cambridge University Press. This book was released on 2005-01-17 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2005 volume brings together twelve papers by many of the most prominent applied general equilibrium modelers honoring Herbert Scarf, the father of equilibrium computation in economics. It deals with developments in applied general equilibrium, a field which has broadened greatly since the 1980s. The contributors discuss some traditional as well as some modern topics in the field, including non-convexities in economy-wide models, tax policy, developmental modeling and energy modeling. The book also covers a range of distinct approaches, conceptual issues and computational algorithms, such as calibration and areas of application such as macroeconomics of real business cycles and finance. An introductory chapter written by the editors maps out issues and scenarios for the future evolution of applied general equilibrium.
Download or read book Interior Point Algorithms written by Yinyu Ye and published by John Wiley & Sons. This book was released on 2011-10-11 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first comprehensive review of the theory and practice of one oftoday's most powerful optimization techniques. The explosive growth of research into and development of interiorpoint algorithms over the past two decades has significantlyimproved the complexity of linear programming and yielded some oftoday's most sophisticated computing techniques. This book offers acomprehensive and thorough treatment of the theory, analysis, andimplementation of this powerful computational tool. Interior Point Algorithms provides detailed coverage of all basicand advanced aspects of the subject. Beginning with an overview offundamental mathematical procedures, Professor Yinyu Ye movesswiftly on to in-depth explorations of numerous computationalproblems and the algorithms that have been developed to solve them.An indispensable text/reference for students and researchers inapplied mathematics, computer science, operations research,management science, and engineering, Interior Point Algorithms: * Derives various complexity results for linear and convexprogramming * Emphasizes interior point geometry and potential theory * Covers state-of-the-art results for extension, implementation,and other cutting-edge computational techniques * Explores the hottest new research topics, including nonlinearprogramming and nonconvex optimization.
Download or read book Levenberg Marquardt Algorithms for Nonlinear Equations Multi objective Optimization and Complementarity Problems written by Pradyumn Kumar Shukla and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Programs with Equilibrium Constraints written by Zhi-Quan Luo and published by Cambridge University Press. This book was released on 1996-11-13 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extensive study for an important class of constrained optimisation problems known as Mathematical Programs with Equilibrium Constraints.
Download or read book Point to set Maps and Mathematical Programming written by P. Huard and published by . This book was released on 1979 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differentiable stability in non convex and non differentiable programming; A multivalued approach to the farkas lemma; Extensions of the continuity of point-to-set maps: applications to fixed point algorithms; Composition und union of general algorithms of optimization; Modified lagrangians in convex programming and their generalizations; Extensions of Zangwill's theorem; On the lower semicontinuity of optimal sets in convex parametric optimization; A note on the continuity of the solution set of special dual optimization problems; Asymptotic properties of sequences iteratively generated by point-to-set maps; Generalized equations and their solutions; The fixed point approach to nonlinear programming; Convergence analysis for two-level algorithms of mathematical programming; A comparative study of several general convergence conditions for algorithms modeled by point-to-set maps.
Download or read book Interior Point Methods of Mathematical Programming written by Tamas Terlaky and published by Springer Science & Business Media. This book was released on 1996-09-30 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: One has to make everything as simple as possible but, never more simple. Albert Einstein Discovery consists of seeing what every body has seen and thinking what nobody has thought. Albert S. ent_Gyorgy; The primary goal of this book is to provide an introduction to the theory of Interior Point Methods (IPMs) in Mathematical Programming. At the same time, we try to present a quick overview of the impact of extensions of IPMs on smooth nonlinear optimization and to demonstrate the potential of IPMs for solving difficult practical problems. The Simplex Method has dominated the theory and practice of mathematical pro gramming since 1947 when Dantzig discovered it. In the fifties and sixties several attempts were made to develop alternative solution methods. At that time the prin cipal base of interior point methods was also developed, for example in the work of Frisch (1955), Caroll (1961), Huard (1967), Fiacco and McCormick (1968) and Dikin (1967). In 1972 Klee and Minty made explicit that in the worst case some variants of the simplex method may require an exponential amount of work to solve Linear Programming (LP) problems. This was at the time when complexity theory became a topic of great interest. People started to classify mathematical programming prob lems as efficiently (in polynomial time) solvable and as difficult (NP-hard) problems. For a while it remained open whether LP was solvable in polynomial time or not. The break-through resolution ofthis problem was obtained by Khachijan (1989).
Download or read book Linear Complementarity Linear and Nonlinear Programming written by Katta G. Murty and published by . This book was released on 1988 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Linear Complementarity Problem written by Richard W. Cottle and published by SIAM. This book was released on 2009-08-27 with total page 781 pages. Available in PDF, EPUB and Kindle. Book excerpt: A revised edition of the standard reference on the linear complementarity problem.
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.
