Simplicial Algorithms On The Simplotope

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Simplicial Algorithms on the Simplotope

Author : Timothy M. Doup
Publisher : Springer Science & Business Media
ISBN 13 : 3642466516
Total Pages : 264 pages
Book Rating : 4.6/5 (424 download)

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Book Synopsis Simplicial Algorithms on the Simplotope by : Timothy M. Doup

Download or read book Simplicial Algorithms on the Simplotope written by Timothy M. Doup and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1.1. Introduction Solving systems of nonlinear equations has since long been of great interest to researchers in the field of economics, mathematics, en gineering, and many other professions. Many problems such as finding an equilibrium, a zero point, or a fixed point, can be formulated as the problem of finding a solution to a system of nonlinear equations. There are many methods to solve the nonlinear system such as Newton's method, the homotopy method, and the simplicial method. In this monograph we mainly consider the simplicial method. Traditionally, the zero point and fixed point problem have been solved by iterative methods such as Newton's method and modifications thereof. Among the difficulties which may cause an iterative method to perform inefficiently or even fail are: the lack of good starting points, slow convergence, and the lack of smoothness of the underlying function. These difficulties have been partly overcome by the introduction of homo topy methods.

Triangulations and Simplicial Methods

Author : Chuangyin Dang
Publisher : Springer Science & Business Media
ISBN 13 : 3642487750
Total Pages : 199 pages
Book Rating : 4.6/5 (424 download)

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Book Synopsis Triangulations and Simplicial Methods by : Chuangyin Dang

Download or read book Triangulations and Simplicial Methods written by Chuangyin Dang and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a new type of technique, simplicial methods have yielded extremely important contributions toward solutions of a system of nonlinear equations. Theoretical investigations and numerical tests have shown that the performance of simplicial methods depends critically on the triangulations underlying them. This monograph describes some recent developments in triangulations and simplicial methods. It includes the D1-triangulation and its applications to simplicial methods. As a result, efficiency of simplicial methods has been improved significantly. Thus more effective simplicial methods have been developed.

Adjustment Processes for Exchange Economies and Noncooperative Games

Author : Antoon van den Elzen
Publisher : Springer Science & Business Media
ISBN 13 : 3642481337
Total Pages : 155 pages
Book Rating : 4.6/5 (424 download)

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Book Synopsis Adjustment Processes for Exchange Economies and Noncooperative Games by : Antoon van den Elzen

Download or read book Adjustment Processes for Exchange Economies and Noncooperative Games written by Antoon van den Elzen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a treatise on adjustment processes. We consider price adjustment processes in exchange economies and strategy adjustment processes in noncooperative games. In the most simple version of an exchange economy, i.e. a pure exchange economy, there exist markets on which prices are determined by the demand and supply created by a finite number of consumers willing to exchange their initial endowments in order to maximize their utilities. An equilibrium situation is attained if, for some price vector, demand equals supply in all markets. Starting from a situation not being an equi librium an adjustment process reaches an equilibrium via adaptations of prices. The advantage of the adjustment processes we will present in this monograph is that they exist and converge under far weaker assumptions than existing processes. The second subject concerns the problem of finding Nash equilibria in noncooperative games. A Nash equilibrium is a situation from which no player can improve his position by unilaterally changing his strategy. We present a new algorithm for finding such equilibria. The sequence of stra tegy vectors generated by the algorithm can be interpreted as the path followed by a strategy adjustment process.

An Incremental Algorithm for Betti Numbers of Simplicial Complexes

Author : Cecil Jose A. Delfinado
Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis An Incremental Algorithm for Betti Numbers of Simplicial Complexes by : Cecil Jose A. Delfinado

Download or read book An Incremental Algorithm for Betti Numbers of Simplicial Complexes written by Cecil Jose A. Delfinado and published by . This book was released on 1993 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Numerical Continuation Methods

Author : Eugene L. Allgower
Publisher : SIAM
ISBN 13 : 089871544X
Total Pages : 409 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Introduction to Numerical Continuation Methods by : Eugene L. Allgower

Download or read book Introduction to Numerical Continuation Methods written by Eugene L. Allgower and published by SIAM. This book was released on 2003-01-01 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical continuation methods have provided important contributions toward the numerical solution of nonlinear systems of equations for many years. The methods may be used not only to compute solutions, which might otherwise be hard to obtain, but also to gain insight into qualitative properties of the solutions. Introduction to Numerical Continuation Methods, originally published in 1979, was the first book to provide easy access to the numerical aspects of predictor corrector continuation and piecewise linear continuation methods. Not only do these seemingly distinct methods share many common features and general principles, they can be numerically implemented in similar ways. Introduction to Numerical Continuation Methods also features the piecewise linear approximation of implicitly defined surfaces, the algorithms of which are frequently used in computer graphics, mesh generation, and the evaluation of surface integrals.

Static and Dynamic Aspects of General Disequilibrium Theory

Author : P. Jean-Jacques Herings
Publisher : Springer Science & Business Media
ISBN 13 : 1461562511
Total Pages : 509 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Static and Dynamic Aspects of General Disequilibrium Theory by : P. Jean-Jacques Herings

Download or read book Static and Dynamic Aspects of General Disequilibrium Theory written by P. Jean-Jacques Herings and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical economics uses mathematical tools and reasoning to describe and explain economic reality. At the core of mathematical economics is general equilibrium theory. Static and Dynamic Aspects of General Disequilibrium Theory describes and analyses various general equilibrium models, treating theory from an axiomatic point of view, which may lead to a deeper understanding of problems, may help to avoid incorrect reasoning, and may improve communication within the economic science. This volume consists of four parts, each of which is self-contained. Part I deals with the mathematical and economic preliminaries. Part II considers the static aspects of disequilibrium theory. Part III determines price rigidities endogenously. Finally, Part IV deals with dynamic aspects of disequilibrium theory.

Algebraic and Differential Topology of Robust Stability

Author : Edmond A. Jonckheere
Publisher : Oxford University Press, USA
ISBN 13 : 0195093011
Total Pages : 625 pages
Book Rating : 4.1/5 (95 download)

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Book Synopsis Algebraic and Differential Topology of Robust Stability by : Edmond A. Jonckheere

Download or read book Algebraic and Differential Topology of Robust Stability written by Edmond A. Jonckheere and published by Oxford University Press, USA. This book was released on 1997 with total page 625 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, two seemingly unrelated fields - algebraic topology and robust control - are brought together. The book develops algebraic/differential topology proceeding from an easily motivated control engineering problem, showing the relevance of advanced topological concepts and reconstructing the fundamental concepts of algebraic/differential topology from an application-oriented point of view. It is suitable for graduate students in engineering and/or applied mathematics, and academic researchers.

Computing Equilibria and Fixed Points

Author : Zaifu Yang
Publisher : Springer Science & Business Media
ISBN 13 : 1475748396
Total Pages : 349 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Computing Equilibria and Fixed Points by : Zaifu Yang

Download or read book Computing Equilibria and Fixed Points written by Zaifu Yang and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computing Equilibria and Fixed Points is devoted to the computation of equilibria, fixed points and stationary points. This volume is written with three goals in mind: (i) To give a comprehensive introduction to fixed point methods and to the definition and construction of Gröbner bases; (ii) To discuss several interesting applications of these methods in the fields of general equilibrium theory, game theory, mathematical programming, algebra and symbolic computation; (iii) To introduce several advanced fixed point and stationary point theorems. These methods and topics should be of interest not only to economists and game theorists concerned with the computation and existence of equilibrium outcomes in economic models and cooperative and non-cooperative games, but also to applied mathematicians, computer scientists and engineers dealing with models of highly nonlinear systems of equations (or polynomial equations).

Recent Advances in Nonsmooth Optimization

Author : Ding-Zhu Du
Publisher : World Scientific
ISBN 13 : 9814500410
Total Pages : 480 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Recent Advances in Nonsmooth Optimization by : Ding-Zhu Du

Download or read book Recent Advances in Nonsmooth Optimization written by Ding-Zhu Du and published by World Scientific. This book was released on 1995-09-20 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonsmooth optimization covers the minimization or maximization of functions which do not have the differentiability properties required by classical methods. The field of nonsmooth optimization is significant, not only because of the existence of nondifferentiable functions arising directly in applications, but also because several important methods for solving difficult smooth problems lead directly to the need to solve nonsmooth problems, which are either smaller in dimension or simpler in structure. This book contains twenty five papers written by forty six authors from twenty countries in five continents. It includes papers on theory, algorithms and applications for problems with first-order nondifferentiability (the usual sense of nonsmooth optimization) second-order nondifferentiability, nonsmooth equations, nonsmooth variational inequalities and other problems related to nonsmooth optimization. Contents:Hybrid Methods for Finding the Nearest Euclidean Distance Matrix (S Al-Homidan & R Fletcher)On Generalized Differentiability of Optimal Solutions and Its Application to an Algorithm for Solving Bilevel Optimization Problems (S Dempe)An Elementary Rate of Convergence Proof for the Deep Cut Ellipsoid Algorithm (J B G Frenk & J Gromicho)On Second-Order Directional Derivatives in Nonsmooth Optimization (L R Huang & K F Ng)Sensitivity of Solutions in Nonlinear Programming Problems with Nonunique Multipliers (A B Levy & R T Rockafellar)Necessary and Sufficient Conditions for Solution Stability of Parametric Nonsmooth Equations (J-S Pang)Characterizations of Optimality for Homogeneous Programming Problems with Applications (A M Rubinov & B M Glover)A Globally Convergent Newton Method for Solving Variational Inequality Problems with Inequality Constraints (K Taji & M Fukushima)A Successive Approximation Quasi-Newton Process for Nonlinear Complementarity Problem (S-Z Zhou et al.)and other papers Readership: Students, academics and industry professionals. keywords:

Adaptive Learning by Genetic Algorithms

Author : Herbert Dawid
Publisher : Springer Science & Business Media
ISBN 13 : 3662002116
Total Pages : 173 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Adaptive Learning by Genetic Algorithms by : Herbert Dawid

Download or read book Adaptive Learning by Genetic Algorithms written by Herbert Dawid and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: An analysis of the learning behavior of genetic algorithms in economic systems with mutual interaction, such as markets. These systems are characterized by a state-dependent fitness function and - for the first time - mathematical results characterizing the long-term outcome of genetic learning in such systems are provided. The usefulness of such results is illustrated by many simulations in evolutionary games and economic models.

Automatic Control in Aerospace 1994 (Aerospace Control '94)

Author : D. Schaechter
Publisher : Elsevier
ISBN 13 : 148329692X
Total Pages : 438 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Automatic Control in Aerospace 1994 (Aerospace Control '94) by : D. Schaechter

Download or read book Automatic Control in Aerospace 1994 (Aerospace Control '94) written by D. Schaechter and published by Elsevier. This book was released on 2014-05-23 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: An important, successful area for control systems development is that of state-of-the-art aeronautical and space related technologies. Leading researchers and practitioners within this field have been given the opportunity to exchange ideas and discuss results at the IFAC symposia on automatic control in aerospace. The key research papers presented at the latest in the series have been put together in this publication to provide a detailed assessment of present and future developments of these control system technologies.

Fuzzy Mathematical Programming

Author : Young-Jou Lai
Publisher : Springer Science & Business Media
ISBN 13 : 364248753X
Total Pages : 317 pages
Book Rating : 4.6/5 (424 download)

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Book Synopsis Fuzzy Mathematical Programming by : Young-Jou Lai

Download or read book Fuzzy Mathematical Programming written by Young-Jou Lai and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last 25 years, the fuzzy set theory has been applied in many disciplines such as operations research, management science, control theory,artificial intelligence/expert system, etc. In this volume, methods and applications of fuzzy mathematical programming and possibilistic mathematical programming are first systematically and thoroughly reviewed and classified. This state-of-the-art survey provides readers with a capsule look into the existing methods, and their characteristics and applicability to analysis of fuzzy and possibilistic programming problems. To realize practical fuzzy modelling, we present solutions for real-world problems including production/manufacturing, transportation, assignment, game, environmental management, resource allocation, project investment, banking/finance, and agricultural economics. To improve flexibility and robustness of fuzzy mathematical programming techniques, we also present our expert decision-making support system IFLP which considers and solves all possibilities of a specific domain of (fuzzy) linear programming problems. Basic fuzzy set theories, membership functions, fuzzy decisions, operators and fuzzy arithmetic are introduced with simple numerical examples in aneasy-to-read and easy-to-follow manner. An updated bibliographical listing of 60 books, monographs or conference proceedings, and about 300 selected papers, reports or theses is presented in the end of this study.

Stochastic Two-Stage Programming

Author : Karl Frauendorfer
Publisher : Springer Science & Business Media
ISBN 13 : 3642956963
Total Pages : 236 pages
Book Rating : 4.6/5 (429 download)

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Book Synopsis Stochastic Two-Stage Programming by : Karl Frauendorfer

Download or read book Stochastic Two-Stage Programming written by Karl Frauendorfer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Programming offers models and methods for decision problems wheresome of the data are uncertain. These models have features and structural properties which are preferably exploited by SP methods within the solution process. This work contributes to the methodology for two-stagemodels. In these models the objective function is given as an integral, whose integrand depends on a random vector, on its probability measure and on a decision. The main results of this work have been derived with the intention to ease these difficulties: After investigating duality relations for convex optimization problems with supply/demand and prices being treated as parameters, a stability criterion is stated and proves subdifferentiability of the value function. This criterion is employed for proving the existence of bilinear functions, which minorize/majorize the integrand. Additionally, these minorants/majorants support the integrand on generalized barycenters of simplicial faces of specially shaped polytopes and amount to an approach which is denoted barycentric approximation scheme.

Computing Economic Equilibria by Variable Dimension Algorithms

Author : G. van der Laan
Publisher :
ISBN 13 :
Total Pages : 58 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Computing Economic Equilibria by Variable Dimension Algorithms by : G. van der Laan

Download or read book Computing Economic Equilibria by Variable Dimension Algorithms written by G. van der Laan and published by . This book was released on 1987 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Simplicial Algorithms for Minimizing Polyhedral Functions

Author : M. R. Osborne
Publisher : Cambridge University Press
ISBN 13 : 9780521791335
Total Pages : 274 pages
Book Rating : 4.7/5 (913 download)

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Book Synopsis Simplicial Algorithms for Minimizing Polyhedral Functions by : M. R. Osborne

Download or read book Simplicial Algorithms for Minimizing Polyhedral Functions written by M. R. Osborne and published by Cambridge University Press. This book was released on 2001-01-08 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2001, provides a general account of the development of simplicial algorithms.

Parallel Computing and Mathematical Optimization

Author : Manfred Grauer
Publisher : Springer Science & Business Media
ISBN 13 : 3642956653
Total Pages : 214 pages
Book Rating : 4.6/5 (429 download)

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Book Synopsis Parallel Computing and Mathematical Optimization by : Manfred Grauer

Download or read book Parallel Computing and Mathematical Optimization written by Manfred Grauer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This special volume contains the Proceedings of a Workshop on "Parallel Algorithms and Transputers for Optimization" which was held at the University of Siegen, on November 9, 1990. The purpose of the Workshop was to bring together those doing research on 2.lgorithms for parallel and distributed optimization and those representatives from industry and business who have an increasing demand for computing power and who may be the potential users of nonsequential approaches. In contrast to many other conferences, especially North-American, on parallel processing and supercomputers the main focus of the contributions and discussion was "problem oriented". This view reflects the following philosophy: How can the existing computing infrastructure (PC's, workstations, local area networks) of an institution or a company be used for parallel and/or distributed problem solution in optimization. This volume of the LECfURE NOTES ON ECONOMICS AND MA THEMA TICAL SYSTEMS contains most of the papers presented at the workshop, plus some additional invited papers covering other important topics related to this workshop. The papers appear here grouped according to four general areas. (1) Solution of optimization problems using massive parallel systems (data parallelism). The authors of these papers are: Lootsma; Gehne. (II) Solution of optimization problems using coarse-grained parallel approaches on multiprocessor systems (control parallelism). The authors of these papers are: Bierwirth, Mattfeld, and Stoppler; Schwartz; Boden, Gehne, and Grauer; and Taudes and Netousek.

Control of Uncertain Dynamic Systems

Author : Shankar P. Bhattacharyya
Publisher : CRC Press
ISBN 13 : 9780849301957
Total Pages : 546 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Control of Uncertain Dynamic Systems by : Shankar P. Bhattacharyya

Download or read book Control of Uncertain Dynamic Systems written by Shankar P. Bhattacharyya and published by CRC Press. This book was released on 1991-10-24 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of 34 papers presented by leading researchers at the International Workshop on Robust Control held in San Antonio, Texas in March 1991. The common theme tying these papers together is the analysis, synthesis, and design of control systems subject to various uncertainties. The papers describe the latest results in parametric understanding, H8 uncertainty, l1 optical control, and Quantitative Feedback Theory (QFT). The book is the first to bring together all the diverse points of view addressing the robust control problem and should strongly influence development in the robust control field for years to come. For this reason, control theorists, engineers, and applied mathematicians should consider it a crucial acquisition for their libraries.