Mathematical Programming Methods

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Methods and Models in Mathematical Programming

S. A. MirHassani,F. Hooshmand
Methods and Models in Mathematical Programming Book PDF

Author : S. A. MirHassani,F. Hooshmand
Publisher : Springer Nature
Page : 389 pages
File Size : 47,7 Mb
Release : 2019-12-09
Category : Mathematics
ISBN : 9783030270452

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Methods and Models in Mathematical Programming by S. A. MirHassani,F. Hooshmand Pdf

This book focuses on mathematical modeling, describes the process of constructing and evaluating models, discusses the challenges and delicacies of the modeling process, and explicitly outlines the required rules and regulations so that the reader will be able to generalize and reuse concepts in other problems by relying on mathematical logic.Undergraduate and postgraduate students of different academic disciplines would find this book a suitable option preparing them for jobs and research fields requiring modeling techniques. Furthermore, this book can be used as a reference book for experts and practitioners requiring advanced skills of model building in their jobs.

Decomposition Techniques in Mathematical Programming

Antonio J. Conejo,Enrique Castillo,Roberto Minguez,Raquel Garcia-Bertrand
Decomposition Techniques in Mathematical Programming Book PDF

Author : Antonio J. Conejo,Enrique Castillo,Roberto Minguez,Raquel Garcia-Bertrand
Publisher : Springer Science & Business Media
Page : 542 pages
File Size : 54,6 Mb
Release : 2006-04-28
Category : Technology & Engineering
ISBN : 9783540276869

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Decomposition Techniques in Mathematical Programming by Antonio J. Conejo,Enrique Castillo,Roberto Minguez,Raquel Garcia-Bertrand Pdf

Optimization plainly dominates the design, planning, operation, and c- trol of engineering systems. This is a book on optimization that considers particular cases of optimization problems, those with a decomposable str- ture that can be advantageously exploited. Those decomposable optimization problems are ubiquitous in engineering and science applications. The book considers problems with both complicating constraints and complicating va- ables, and analyzes linear and nonlinear problems, with and without in- ger variables. The decomposition techniques analyzed include Dantzig-Wolfe, Benders, Lagrangian relaxation, Augmented Lagrangian decomposition, and others. Heuristic techniques are also considered. Additionally, a comprehensive sensitivity analysis for characterizing the solution of optimization problems is carried out. This material is particularly novel and of high practical interest. This book is built based on many clarifying, illustrative, and compu- tional examples, which facilitate the learning procedure. For the sake of cl- ity, theoretical concepts and computational algorithms are assembled based on these examples. The results are simplicity, clarity, and easy-learning. We feel that this book is needed by the engineering community that has to tackle complex optimization problems, particularly by practitioners and researchersinEngineering,OperationsResearch,andAppliedEconomics.The descriptions of most decomposition techniques are available only in complex and specialized mathematical journals, di?cult to understand by engineers. A book describing a wide range of decomposition techniques, emphasizing problem-solving, and appropriately blending theory and application, was not previously available.

Mathematical Programming Methods

G. Zoutendijk
Mathematical Programming Methods Book PDF

Author : G. Zoutendijk
Publisher : Unknown
Page : 524 pages
File Size : 50,9 Mb
Release : 1976
Category : Mathematics
ISBN : UCAL:B4406042

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Mathematical Programming Methods by G. Zoutendijk Pdf

Theory of linear programming; The simplex method; Numerical aspects of the simplex method; Other methods for linear programming; Special structures; Post-optimal analysis; Decomposition and partitioning methods; Integer and mixed integer linear programming; Theory of nonlinear programming; General principles of a method of feasible directions; Direction generators; Linear programming and the methods of feasible directions; Unconstrained optimization; Quadratic programming; Linearly constrained nonlinear programming; General nonlinear programming.

Progress in Mathematical Programming

Nimrod Megiddo
Progress in Mathematical Programming Book PDF

Author : Nimrod Megiddo
Publisher : Springer Science & Business Media
Page : 164 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461396178

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Progress in Mathematical Programming by Nimrod Megiddo Pdf

The starting point of this volume was a conference entitled "Progress in Mathematical Programming," held at the Asilomar Conference Center in Pacific Grove, California, March 1-4, 1987. The main topic of the conference was developments in the theory and practice of linear programming since Karmarkar's algorithm. There were thirty presentations and approximately fifty people attended. Presentations included new algorithms, new analyses of algorithms, reports on computational experience, and some other topics related to the practice of mathematical programming. Interestingly, most of the progress reported at the conference was on the theoretical side. Several new polynomial algorithms for linear program ming were presented (Barnes-Chopra-Jensen, Goldfarb-Mehrotra, Gonzaga, Kojima-Mizuno-Yoshise, Renegar, Todd, Vaidya, and Ye). Other algorithms presented were by Betke-Gritzmann, Blum, Gill-Murray-Saunders-Wright, Nazareth, Vial, and Zikan-Cottle. Efforts in the theoretical analysis of algo rithms were also reported (Anstreicher, Bayer-Lagarias, Imai, Lagarias, Megiddo-Shub, Lagarias, Smale, and Vanderbei). Computational experiences were reported by Lustig, Tomlin, Todd, Tone, Ye, and Zikan-Cottle. Of special interest, although not in the main direction discussed at the conference, was the report by Rinaldi on the practical solution of some large traveling salesman problems. At the time of the conference, it was still not clear whether the new algorithms developed since Karmarkar's algorithm would replace the simplex method in practice. Alan Hoffman presented results on conditions under which linear programming problems can be solved by greedy algorithms."

Modelling in Mathematical Programming

José Manuel García Sánchez
Modelling in Mathematical Programming Book PDF

Author : José Manuel García Sánchez
Publisher : Springer Nature
Page : 291 pages
File Size : 41,7 Mb
Release : 2020-10-31
Category : Business & Economics
ISBN : 9783030572501

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Modelling in Mathematical Programming by José Manuel García Sánchez Pdf

This book provides basic tools for learning how to model in mathematical programming, from models without much complexity to complex system models. It presents a unique methodology for the building of an integral mathematical model, as well as new techniques that help build under own criteria. It allows readers to structure models from the elements and variables to the constraints, a basic modelling guide for any system with a new scheme of variables, a classification of constraints and also a set of rules to model specifications stated as logical propositions, helping to better understand models already existing in the literature. It also presents the modelling of all possible objectives that may arise in optimization problems regarding the variables values. The book is structured to guide the reader in an orderly manner, learning of the components that the methodology establishes in an optimization problem. The system includes the elements, which are all the actors that participate in the system, decision activities that occur in the system, calculations based on the decision activities, specifications such as regulations, impositions or actions of defined value and objective criterion, which guides the resolution of the system.

Interior Point Methods of Mathematical Programming

Tamás Terlaky
Interior Point Methods of Mathematical Programming Book PDF

Author : Tamás Terlaky
Publisher : Springer Science & Business Media
Page : 544 pages
File Size : 40,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461334491

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Interior Point Methods of Mathematical Programming by Tamás Terlaky Pdf

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).

Fuzzy Mathematical Programming

Young-Jou Lai,Ching-Lai Hwang
Fuzzy Mathematical Programming Book PDF

Author : Young-Jou Lai,Ching-Lai Hwang
Publisher : Springer Science & Business Media
Page : 317 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642487538

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Fuzzy Mathematical Programming by Young-Jou Lai,Ching-Lai Hwang Pdf

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.

Mathematical Programming Methods for Geographers and Planners

James Killen
Mathematical Programming Methods for Geographers and Planners Book PDF

Author : James Killen
Publisher : Routledge
Page : 386 pages
File Size : 50,6 Mb
Release : 2021-12-01
Category : Computers
ISBN : 9781000397420

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Mathematical Programming Methods for Geographers and Planners by James Killen Pdf

Originally published in 1983, this was the first text to offer an in-depth treatment of mathematical programming methods explained from first principles. It considers all the major programming techniques and fully explains key terms, illustrates theories with detailed examples and shows how the various skills are applied in practice. It will be invaluable in both the academic world and to policy formulators and planners, who make extensive use of the methods described.

Mathematical Programming

S. M. Sinha
Mathematical Programming Book PDF

Author : S. M. Sinha
Publisher : Elsevier
Page : 572 pages
File Size : 54,6 Mb
Release : 2005-01-01
Category : Mathematics
ISBN : 0080535933

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Mathematical Programming by S. M. Sinha Pdf

Mathematical Programming, a branch of Operations Research, is perhaps the most efficient technique in making optimal decisions. It has a very wide application in the analysis of management problems, in business and industry, in economic studies, in military problems and in many other fields of our present day activities. In this keen competetive world, the problems are getting more and more complicated ahnd efforts are being made to deal with these challenging problems. This book presents from the origin to the recent developments in mathematical programming. The book has wide coverage and is self-contained. It is suitable both as a text and as a reference. * A wide ranging all encompasing overview of mathematical programming from its origins to recent developments * A result of over thirty years of teaching experience in this feild * A self-contained guide suitable both as a text and as a reference

Mathematical Programming Methods in Structural Plasticity

D. Lloyd Smith
Mathematical Programming Methods in Structural Plasticity Book PDF

Author : D. Lloyd Smith
Publisher : Springer
Page : 433 pages
File Size : 45,8 Mb
Release : 2014-05-04
Category : Technology & Engineering
ISBN : 9783709126189

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Mathematical Programming Methods in Structural Plasticity by D. Lloyd Smith Pdf

Civil engineering structures tend to be fabricated from materials that respond elastically at normal levels of loading. Most such materials, however, would exhibit a marked and ductile inelasticity if the structure were overloaded by accident or by some improbable but naturally occuring phenomeon. Indeed, the very presence of such ductility constitutes an important safety provision for large-scale constructions where human life is at risk. In the comprehensive evaluation of safety in structural design, it is therefore unrealistic not to consider the effects of ductility. This book sets out to show that the bringing together of the theory and methods of mathematical programming with the mathematical theory of plasticity furnishes a model which has a unifying theoretical nature and is entirely representative of observed structural behaviour. The contents of the book provide a review of the relevant aspects of mathematical programming and plasticity theory, together with a detailed presentation of the most interesting and potentially useful applications in both framed and continuum structures: ultimate strength and elastoplastic deformability; shakedown and practical upper bounds on deformation measures; evolutive dynamic response; large displacements and instability; stochastic and fuzzy programming for representing uncertainty in ultimate strength calculations. Besides providing a ready fund of computational algorithms, mathematical programming invests applications in mechanics with a refined mathematical formalism, rich in fundamental theorems, which often gives addi- tional insight into known results and occasionally lead to new ones. In addition to its obvious practical utility, the educational value of the material thoroughly befits a university discipline.

Nondifferentiable and Two-Level Mathematical Programming

Kiyotaka Shimizu,Yo Ishizuka,Jonathan F. Bard
Nondifferentiable and Two Level Mathematical Programming Book PDF

Author : Kiyotaka Shimizu,Yo Ishizuka,Jonathan F. Bard
Publisher : Springer Science & Business Media
Page : 482 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9781461563051

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Nondifferentiable and Two-Level Mathematical Programming by Kiyotaka Shimizu,Yo Ishizuka,Jonathan F. Bard Pdf

The analysis and design of engineering and industrial systems has come to rely heavily on the use of optimization techniques. The theory developed over the last 40 years, coupled with an increasing number of powerful computational procedures, has made it possible to routinely solve problems arising in such diverse fields as aircraft design, material flow, curve fitting, capital expansion, and oil refining just to name a few. Mathematical programming plays a central role in each of these areas and can be considered the primary tool for systems optimization. Limits have been placed on the types of problems that can be solved, though, by the difficulty of handling functions that are not everywhere differentiable. To deal with real applications, it is often necessary to be able to optimize functions that while continuous are not differentiable in the classical sense. As the title of the book indicates, our chief concern is with (i) nondifferentiable mathematical programs, and (ii) two-level optimization problems. In the first half of the book, we study basic theory for general smooth and nonsmooth functions of many variables. After providing some background, we extend traditional (differentiable) nonlinear programming to the nondifferentiable case. The term used for the resultant problem is nondifferentiable mathematical programming. The major focus is on the derivation of optimality conditions for general nondifferentiable nonlinear programs. We introduce the concept of the generalized gradient and derive Kuhn-Tucker-type optimality conditions for the corresponding formulations.

Applied Mathematical Programming

Stephen P. Bradley,Arnoldo C. Hax,Thomas L. Magnanti
Applied Mathematical Programming Book PDF

Author : Stephen P. Bradley,Arnoldo C. Hax,Thomas L. Magnanti
Publisher : Addison Wesley Publishing Company
Page : 748 pages
File Size : 45,9 Mb
Release : 1977
Category : Mathematics
ISBN : MINN:31951001006972E

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Applied Mathematical Programming by Stephen P. Bradley,Arnoldo C. Hax,Thomas L. Magnanti Pdf

Mathematical programming: an overview; solving linear programs; sensitivity analysis; duality in linear programming; mathematical programming in practice; integration of strategic and tactical planning in the aluminum industry; planning the mission and composition of the U.S. merchant Marine fleet; network models; integer programming; design of a naval tender job shop; dynamic programming; large-scale systems; nonlinear programming; a system for bank portfolio planning; vectors and matrices; linear programming in matrix form; a labeling algorithm for the maximun-flow network problem.

Fractional Programming

I.M. Stancu-Minasian
Fractional Programming Book PDF

Author : I.M. Stancu-Minasian
Publisher : Springer Science & Business Media
Page : 430 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400900356

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Fractional Programming by I.M. Stancu-Minasian Pdf

Mathematical programming has know a spectacular diversification in the last few decades. This process has happened both at the level of mathematical research and at the level of the applications generated by the solution methods that were created. To write a monograph dedicated to a certain domain of mathematical programming is, under such circumstances,especially difficult. In the present monograph we opt for the domain of fractional programming. Interest of this subject was generated by the fact that various optimization problems from engineering and economics consider the minimization of a ratio between physical and/or economical functions, for example cost/time, cost/volume,cost/profit, or other quantities that measure the efficiency of a system. For example, the productivity of industrial systems, defined as the ratio between the realized services in a system within a given period of time and the utilized resources, is used as one of the best indicators of the quality of their operation. Such problems, where the objective function appears as a ratio of functions, constitute fractional programming problem. Due to its importance in modeling various decision processes in management science, operational research, and economics, and also due to its frequent appearance in other problems that are not necessarily economical, such as information theory, numerical analysis, stochastic programming, decomposition algorithms for large linear systems, etc., the fractional programming method has received particular attention in the last three decades.

Mathematical Methods in Program Development

Manfred Broy,Birgit Schieder
Mathematical Methods in Program Development Book PDF

Author : Manfred Broy,Birgit Schieder
Publisher : Springer Science & Business Media
Page : 538 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642608582

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Mathematical Methods in Program Development by Manfred Broy,Birgit Schieder Pdf

Modern information processing systems show such complex properties as distribution, parallelism, interaction, time dependency, and nondeterminism. For critical applications, mathematical methods are needed to model the systems and to support their development and validation. Impressive progress in mathematical methods for programming software systems makes it possible to think about unifying the different approaches. This book gives a comprehensive overview of existing methods and presents some of the most recent results in applying them. The main topics are: advanced programming techniques, foundations of systems engineering, mathematical support methods, and application of the methods. The approaches presented are illustrated by examples and related to other approaches.

Economic Foundations of Symmetric Programming

Quirino Paris
Economic Foundations of Symmetric Programming Book PDF

Author : Quirino Paris
Publisher : Cambridge University Press
Page : 569 pages
File Size : 48,8 Mb
Release : 2010-11-01
Category : Business & Economics
ISBN : 9781139492294

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Economic Foundations of Symmetric Programming by Quirino Paris Pdf

The search for symmetry is part of the fundamental scientific paradigm in mathematics and physics. Can this be valid also for economics? This book represents an attempt to explore this possibility. The behavior of price-taking producers, monopolists, monopsonists, sectoral market equilibria, behavior under risk and uncertainty, and two-person zero- and non-zero-sum games are analyzed and discussed under the unifying structure called the linear complementarity problem. Furthermore, the equilibrium problem allows for the relaxation of often-stated but unnecessary assumptions. This unifying approach offers the advantage of a better understanding of the structure of economic models. It also introduces the simplest and most elegant algorithm for solving a wide class of problems.