Algebraic and Geometric Ideas in the Theory of Discrete Optimization PDF Download
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Author: Jesus A. De Loera
Publisher: SIAM
ISBN: 1611972434
Category : Mathematics
Languages : en
Pages : 320
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Book Description
In recent years, many new techniques have emerged in the mathematical theory of discrete optimization that have proven to be effective in solving a number of hard problems. This book presents these recent advances, particularly those that arise from algebraic geometry, commutative algebra, convex and discrete geometry, generating functions, and other tools normally considered outside of the standard curriculum in optimization. These new techniques, all of which are presented with minimal prerequisites, provide a transition from linear to nonlinear discrete optimization. This book can be used as a textbook for advanced undergraduates or first-year graduate students in mathematics, computer science or operations research. It is also appropriate for mathematicians, engineers, and scientists engaged in computation who wish to gain a deeper understanding of how and why algorithms work.
Author: Jesus A. De Loera
Publisher: SIAM
ISBN: 1611972434
Category : Mathematics
Languages : en
Pages : 320
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Book Description
In recent years, many new techniques have emerged in the mathematical theory of discrete optimization that have proven to be effective in solving a number of hard problems. This book presents these recent advances, particularly those that arise from algebraic geometry, commutative algebra, convex and discrete geometry, generating functions, and other tools normally considered outside of the standard curriculum in optimization. These new techniques, all of which are presented with minimal prerequisites, provide a transition from linear to nonlinear discrete optimization. This book can be used as a textbook for advanced undergraduates or first-year graduate students in mathematics, computer science or operations research. It is also appropriate for mathematicians, engineers, and scientists engaged in computation who wish to gain a deeper understanding of how and why algorithms work.
Author: David Gottlieb
Publisher: SIAM
ISBN: 0898710235
Category : Technology & Engineering
Languages : en
Pages : 167
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Book Description
A unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting extensions of the classical numerical analysis.
Author: Mokhtar S. Bazaraa
Publisher: John Wiley & Sons
ISBN: 0471486000
Category : Mathematics
Languages : en
Pages : 885
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Book Description
COMPREHENSIVE COVERAGE OF NONLINEAR PROGRAMMING THEORY AND ALGORITHMS, THOROUGHLY REVISED AND EXPANDED Nonlinear Programming: Theory and Algorithms—now in an extensively updated Third Edition—addresses the problem of optimizing an objective function in the presence of equality and inequality constraints. Many realistic problems cannot be adequately represented as a linear program owing to the nature of the nonlinearity of the objective function and/or the nonlinearity of any constraints. The Third Edition begins with a general introduction to nonlinear programming with illustrative examples and guidelines for model construction. Concentration on the three major parts of nonlinear programming is provided: Convex analysis with discussion of topological properties of convex sets, separation and support of convex sets, polyhedral sets, extreme points and extreme directions of polyhedral sets, and linear programming Optimality conditions and duality with coverage of the nature, interpretation, and value of the classical Fritz John (FJ) and the Karush-Kuhn-Tucker (KKT) optimality conditions; the interrelationships between various proposed constraint qualifications; and Lagrangian duality and saddle point optimality conditions Algorithms and their convergence, with a presentation of algorithms for solving both unconstrained and constrained nonlinear programming problems Important features of the Third Edition include: New topics such as second interior point methods, nonconvex optimization, nondifferentiable optimization, and more Updated discussion and new applications in each chapter Detailed numerical examples and graphical illustrations Essential coverage of modeling and formulating nonlinear programs Simple numerical problems Advanced theoretical exercises The book is a solid reference for professionals as well as a useful text for students in the fields of operations research, management science, industrial engineering, applied mathematics, and also in engineering disciplines that deal with analytical optimization techniques. The logical and self-contained format uniquely covers nonlinear programming techniques with a great depth of information and an abundance of valuable examples and illustrations that showcase the most current advances in nonlinear problems.
Author: Kenneth Joseph Arrow
Publisher: Gulf Professional Publishing
ISBN: 9780444829146
Category : Social choice
Languages : en
Pages : 686
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Book Description
The Handbook of Social Choice and Welfare presents, in two volumes, essays on past and on-going work in social choice theory and welfare economics. The first volume consists of four parts. In Part 1 (Arrovian Impossibility Theorems), various aspects of Arrovian general impossibility theorems, illustrated by the simple majority cycle first identified by Condorcet, are expounded and evaluated. It also provides a critical survey of the work on different escape routes from impossibility results of this kind. In Part 2 (Voting Schemes and Mechanisms), the operation and performance of voting schemes and cost-sharing mechanisms are examined axiomatically, and some aspects of the modern theory of incentives and mechanism design are expounded and surveyed. In Part 3 (structure of social choice rules), the positional rules of collective decision-making (the origin of which can be traced back to a seminal proposal by Borda), the game-theoretic aspects of voting in committees, and the implications of making use of interpersonal comparisons of welfare (with or without cardinal measurability) are expounded, and the status of utilitarianism as a theory of justice is critically examined. It also provides an analytical survey of the foundations of measurement of inequality and poverty. In order to place these broad issues (as well as further issues to be discussed in the second volume of the Handbook) in perspective, Kotaro Suzumura has written an extensive introduction, discussing the historical background of social choice theory, the vistas opened by Arrow's Social Choice and Individual Values, the famous "socialist planning" controversy, and the theoretical and practical significance of social choice theory. The primary purpose of this Handbook is to provide an accessible introduction to the current state of the art in social choice theory and welfare economics. The expounded theory has a strong and constructive message for pursuing human well-being and facilitating collective decision-making. *Advances economists' understanding of recent advances in social choice and welfare *Distills and applies research to a wide range of social issues *Provides analytical material for evaluating new scholarship *Offers consolidated reviews and analyses of scholarship in a framework that encourages synthesis--
Author: Matthias Gerdts
Publisher: Walter de Gruyter
ISBN: 3110249995
Category : Mathematics
Languages : en
Pages : 469
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Book Description
The intention of this textbook is to provide both, the theoretical and computational tools that are necessary to investigate and to solve optimal control problems with ordinary differential equations and differential-algebraic equations. An emphasis is placed on the interplay between the continuous optimal control problem, which typically is defined and analyzed in a Banach space setting, and discrete optimal control problems, which are obtained by discretization and lead to finite dimensional optimization problems. The book addresses primarily master and PhD students as well as researchers in applied mathematics, but also engineers or scientists with a good background in mathematics and interest in optimal control. The theoretical parts of the book require some knowledge of functional analysis, the numerically oriented parts require knowledge from linear algebra and numerical analysis. Examples are provided for illustration purposes.
Author: National Institute of Standards and Technology (U.S.)
Publisher:
ISBN:
Category : Engineering
Languages : en
Pages : 268
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Book Description
Author: Charles J. Alpert
Publisher: CRC Press
ISBN: 1000654192
Category : Computers
Languages : en
Pages : 1044
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Book Description
The physical design flow of any project depends upon the size of the design, the technology, the number of designers, the clock frequency, and the time to do the design. As technology advances and design-styles change, physical design flows are constantly reinvented as traditional phases are removed and new ones are added to accommodate changes in
Author: Michel Cosnard
Publisher: Springer Science & Business Media
ISBN: 9783540580782
Category : Computers
Languages : en
Pages : 296
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Book Description
This volume presents the proceedings of the First Canada-France Conference on Parallel Computing; despite its name, this conference was open to full international contribution and participation, as shown by the list of contributing authors. This volume consists of in total 22 full papers, either invited or accepted and revised after a thorough reviewing process. All together the papers provide a highly competent perspective on research in parallel algorithms and complexity, interconnection networks and distributed computing, algorithms for unstructured problems, and structured communications from the point of view of parallel and distributed computing.
Author: Alexander Schrijver
Publisher: Springer Science & Business Media
ISBN: 9783540443896
Category : Business & Economics
Languages : en
Pages : 2024
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Book Description
From the reviews: "About 30 years ago, when I was a student, the first book on combinatorial optimization came out referred to as "the Lawler" simply. I think that now, with this volume Springer has landed a coup: "The Schrijver". The box is offered for less than 90.- EURO, which to my opinion is one of the best deals after the introduction of this currency." OR-Spectrum
Author: Ulrik Brandes
Publisher: Springer
ISBN: 3540400648
Category : Computers
Languages : en
Pages : 324
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Book Description
The 26th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2000) was held at Waldhaus Jakob, in Konstanz, Germany, on 15{ 17 June 2000. It was organized by the Algorithms and Data Structures Group of the Department of Computer and Information Science, University of K- stanz, and sponsored by Deutsche Forschungsgemeinschaft (DFG) and Univ- sit ̈atsgesellschaft Konstanz. The workshop aims at uniting theory and practice by demonstrating how graph-theoretic concepts can be applied to various areas in computer science, or by extracting new problems from applications. The goal is to present recent research results and to identify and explore directions for future research. The workshop looks back on a remarkable tradition of more than a quarter of a century. Previous Workshops have been organized in various places in Europe, and submissions come from all over the world. This year, 57 attendees from 13 di erent countries gathered in the relaxing atmosphere of Lake Constance, also known as the Bodensee. Out of 51 submis- ons, the program committee carefully selected 26 papers for presentation at the workshop. This selection re?ects current research directions, among them graph and network algorithms and their complexity, algorithms for special graph cl- ses, communication networks, and distributed algorithms. The present volume contains these papers together with the survey presented in an invited lecture by Ingo Wegener (University of Dortmund) and an extended abstract of the invited lecture given by Emo Welzl (ETH Zuric ̈ h).
