Nonlinear Programming

Author: Dimitri P. Bertsekas

Publisher: N.A

ISBN: 9781886529052

Category: Mathematical optimization

Page: 859

View: 8225

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The third edition of the book is a thoroughly rewritten version of the 1999 2nd edition. New material was included, some of the old material was discarded, and a large portion of the remainder was reorganized or revised. This book provides a comprehensive and accessible presentation of algorithms for solving continuous optimization problems. It relies on rigorous mathematical analysis, but also aims at an intuitive exposition that makes use of visualization where possible. It places particular emphasis on modern developments, and their widespread applications in fields such as large-scale resource allocation problems, signal processing, and machine learning. The book was developed through instruction at MIT, focuses on nonlinear and other types of optimization: iterative algorithms for constrained and unconstrained optimization, Lagrange multipliers and duality, large scale problems, and the interface between continuous and discrete optimization. Among its special features, the book: 1) provides extensive coverage of iterative optimization methods within a unifying framework 2) provides a detailed treatment of interior point methods for linear programming 3) covers in depth duality theory from both a variational and a geometrical/convex analysis point of view 4) includes much new material on a number of topics, such as neural network training, large-scale optimization, signal processing, machine learning, and optimal control 5) includes a large number of examples and exercises detailed solutions of many of which are posted on the internet.

Nonlinear Programming

Theory and Algorithms

Author: Mokhtar S. Bazaraa,Hanif D. Sherali,C. M. Shetty

Publisher: John Wiley & Sons

ISBN: 1118626303

Category: Mathematics

Page: 872

View: 910

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COMPREHENSIVE COVERAGE OF NONLINEAR PROGRAMMING THEORY ANDALGORITHMS, THOROUGHLY REVISED AND EXPANDED Nonlinear Programming: Theory and Algorithms—now inan extensively updated Third Edition—addresses the problem ofoptimizing an objective function in the presence of equality andinequality constraints. Many realistic problems cannot beadequately represented as a linear program owing to the nature ofthe nonlinearity of the objective function and/or the nonlinearityof any constraints. The Third Edition begins with a generalintroduction to nonlinear programming with illustrative examplesand guidelines for model construction. Concentration on the three major parts of nonlinear programmingis provided: Convex analysis with discussion of topological properties ofconvex sets, separation and support of convex sets, polyhedralsets, extreme points and extreme directions of polyhedral sets, andlinear programming Optimality conditions and duality with coverage of the nature,interpretation, and value of the classical Fritz John (FJ) and theKarush-Kuhn-Tucker (KKT) optimality conditions; theinterrelationships between various proposed constraintqualifications; and Lagrangian duality and saddle point optimalityconditions Algorithms and their convergence, with a presentation ofalgorithms for solving both unconstrained and constrained nonlinearprogramming problems Important features of the Third Edition include: New topics such as second interior point methods, nonconvexoptimization, nondifferentiable optimization, and more Updated discussion and new applications in each chapter Detailed numerical examples and graphical illustrations Essential coverage of modeling and formulating nonlinearprograms Simple numerical problems Advanced theoretical exercises The book is a solid reference for professionals as well as auseful text for students in the fields of operations research,management science, industrial engineering, applied mathematics,and also in engineering disciplines that deal with analyticaloptimization techniques. The logical and self-contained formatuniquely covers nonlinear programming techniques with a great depthof information and an abundance of valuable examples andillustrations that showcase the most current advances in nonlinearproblems.

Linear and Nonlinear Programming

Author: David G. Luenberger,Yinyu Ye

Publisher: Springer Science & Business Media

ISBN: 0387745025

Category: Business & Economics

Page: 546

View: 6458

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This third edition of the classic textbook in Optimization has been fully revised and updated. It comprehensively covers modern theoretical insights in this crucial computing area, and will be required reading for analysts and operations researchers in a variety of fields. The book connects the purely analytical character of an optimization problem, and the behavior of algorithms used to solve it. Now, the third edition has been completely updated with recent Optimization Methods. The book also has a new co-author, Yinyu Ye of California’s Stanford University, who has written lots of extra material including some on Interior Point Methods.

Linear and Nonlinear Optimization

Author: Richard W. Cottle,Mukund N. Thapa

Publisher: Springer

ISBN: 1493970550

Category: Business & Economics

Page: 614

View: 9780

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​This textbook on Linear and Nonlinear Optimization is intended for graduate and advanced undergraduate students in operations research and related fields. It is both literate and mathematically strong, yet requires no prior course in optimization. As suggested by its title, the book is divided into two parts covering in their individual chapters LP Models and Applications; Linear Equations and Inequalities; The Simplex Algorithm; Simplex Algorithm Continued; Duality and the Dual Simplex Algorithm; Postoptimality Analyses; Computational Considerations; Nonlinear (NLP) Models and Applications; Unconstrained Optimization; Descent Methods; Optimality Conditions; Problems with Linear Constraints; Problems with Nonlinear Constraints; Interior-Point Methods; and an Appendix covering Mathematical Concepts. Each chapter ends with a set of exercises. The book is based on lecture notes the authors have used in numerous optimization courses the authors have taught at Stanford University. It emphasizes modeling and numerical algorithms for optimization with continuous (not integer) variables. The discussion presents the underlying theory without always focusing on formal mathematical proofs (which can be found in cited references). Another feature of this book is its inclusion of cultural and historical matters, most often appearing among the footnotes. "This book is a real gem. The authors do a masterful job of rigorously presenting all of the relevant theory clearly and concisely while managing to avoid unnecessary tedious mathematical details. This is an ideal book for teaching a one or two semester masters-level course in optimization – it broadly covers linear and nonlinear programming effectively balancing modeling, algorithmic theory, computation, implementation, illuminating historical facts, and numerous interesting examples and exercises. Due to the clarity of the exposition, this book also serves as a valuable reference for self-study." Professor Ilan Adler, IEOR Department, UC Berkeley "A carefully crafted introduction to the main elements and applications of mathematical optimization. This volume presents the essential concepts of linear and nonlinear programming in an accessible format filled with anecdotes, examples, and exercises that bring the topic to life. The authors plumb their decades of experience in optimization to provide an enriching layer of historical context. Suitable for advanced undergraduates and masters students in management science, operations research, and related fields." Michael P. Friedlander, IBM Professor of Computer Science, Professor of Mathematics, University of British Columbia

Operations Research

A Practical Introduction

Author: Michael Carter,Camille C. Price,Ghaith Rabadi

Publisher: CRC Press

ISBN: 1498780121

Category: Business & Economics

Page: 448

View: 4992

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Operations Research: A Practical Introduction is just that: a hands-on approach to the field of operations research (OR) and a useful guide for using OR techniques in scientific decision making, design, analysis and management. The text accomplishes two goals. First, it provides readers with an introduction to standard mathematical models and algorithms. Second, it is a thorough examination of practical issues relevant to the development and use of computational methods for problem solving. Highlights: All chapters contain up-to-date topics and summaries A succinct presentation to fit a one-term course Each chapter has references, readings, and list of key terms Includes illustrative and current applications New exercises are added throughout the text Software tools have been updated with the newest and most popular software Many students of various disciplines such as mathematics, economics, industrial engineering and computer science often take one course in operations research. This book is written to provide a succinct and efficient introduction to the subject for these students, while offering a sound and fundamental preparation for more advanced courses in linear and nonlinear optimization, and many stochastic models and analyses. It provides relevant analytical tools for this varied audience and will also serve professionals, corporate managers, and technical consultants.

Business Analytics with Management Science Models and Methods

Author: Arben Asllani

Publisher: FT Press

ISBN: 0133760669

Category: Business & Economics

Page: 400

View: 873

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Master decision modeling and analytics through realistic examples, intuitive explanations, and tested Excel templates. Business Analytics with Management Science has been designed to help students, practitioners and managers use business analytics to improve decision-making systems. Unlike previous books, it emphasizes the application of practical management science techniques in business analytics. Drawing on 20+ years of teaching and consulting experience, Dr. Arben Asllani introduces decision analytics through realistic examples and intuitive explanations – not complex formulae and theoretical definitions. Throughout, Asllani helps practitioners focus more on the crucial input-output aspects of decision making – and less upon internal model complexities that can usually be "delegated" to software.

Solutions Manual to accompany Nonlinear Programming

Theory and Algorithms

Author: Mokhtar S. Bazaraa,Hanif D. Sherali,C. M. Shetty

Publisher: John Wiley & Sons

ISBN: 1118762320

Category: Mathematics

Page: 174

View: 9375

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As the Solutions Manual, this book is meant to accompany the maintitle, Nonlinear Programming: Theory and Algorithms, ThirdEdition. This book presents recent developments of keytopics in nonlinear programming (NLP) using a logical andself-contained format. The volume is divided into three sections:convex analysis, optimality conditions, and dual computationaltechniques. Precise statements of algortihms are given along withconvergence analysis. Each chapter contains detailed numericalexamples, graphical illustrations, and numerous exercises to aidreaders in understanding the concepts and methods discussed.

Data-Driven Modeling & Scientific Computation

Methods for Complex Systems & Big Data

Author: J. Nathan Kutz

Publisher: OUP Oxford

ISBN: 019163588X

Category: Language Arts & Disciplines

Page: 608

View: 7240

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The burgeoning field of data analysis is expanding at an incredible pace due to the proliferation of data collection in almost every area of science. The enormous data sets now routinely encountered in the sciences provide an incentive to develop mathematical techniques and computational algorithms that help synthesize, interpret and give meaning to the data in the context of its scientific setting. A specific aim of this book is to integrate standard scientific computing methods with data analysis. By doing so, it brings together, in a self-consistent fashion, the key ideas from: · statistics, · time-frequency analysis, and · low-dimensional reductions The blend of these ideas provides meaningful insight into the data sets one is faced with in every scientific subject today, including those generated from complex dynamical systems. This is a particularly exciting field and much of the final part of the book is driven by intuitive examples from it, showing how the three areas can be used in combination to give critical insight into the fundamental workings of various problems. Data-Driven Modeling and Scientific Computation is a survey of practical numerical solution techniques for ordinary and partial differential equations as well as algorithms for data manipulation and analysis. Emphasis is on the implementation of numerical schemes to practical problems in the engineering, biological and physical sciences. An accessible introductory-to-advanced text, this book fully integrates MATLAB and its versatile and high-level programming functionality, while bringing together computational and data skills for both undergraduate and graduate students in scientific computing.

Power Generation, Operation, and Control

Author: Allen J. Wood,Bruce F. Wollenberg,Gerald B. Sheblé

Publisher: John Wiley & Sons

ISBN: 1118733916

Category: Technology & Engineering

Page: 656

View: 7587

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A thoroughly revised new edition of the definitive work on power systems best practices In this eagerly awaited new edition, Power Generation, Operation, and Control continues to provide engineers and academics with a complete picture of the techniques used in modern power system operation. Long recognized as the standard reference in the field, the book has been thoroughly updated to reflect the enormous changes that have taken place in the electric power industry since the Second Edition was published seventeen years ago. With an emphasis on both the engineering and economic aspects of energy management, the Third Edition introduces central "terminal" characteristics for thermal and hydroelectric power generation systems, along with new optimization techniques for tackling real-world operating problems. Readers will find a range of algorithms and methods for performing integrated economic, network, and generating system analysis, as well as modern methods for power system analysis, operation, and control. Special features include: State-of-the-art topics such as market simulation, multiple market analysis, contract and market bidding, and other business topics Chapters on generation with limited energy supply, power flow control, power system security, and more An introduction to regulatory issues, renewable energy, and other evolving topics New worked examples and end-of-chapter problems A companion website with additional materials, including MATLAB programs and power system sample data sets

Optimization Modeling with Spreadsheets

Author: Kenneth R. Baker

Publisher: John Wiley & Sons

ISBN: 1118937694

Category: Business & Economics

Page: 392

View: 3781

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Updated with Microsoft® Office Excel®'s freely available Solver throughout, this Third Edition successfully bridges the gap between the theory and applications of model building for optimization analysis. Thoroughly updated to reflect the latest topical and technical advances in the field, Optimization Modeling with Spreadsheets, Third Edition continues to focus on solving real-world optimization problems through the creation of mathematical models and the use of spreadsheets for analysis. Developed to equip readers with the skills needed to apply optimization tools effectively without the need to rely on specialized algorithms. This introductory book on optimization (mathematical programming) includes coverage on linear programming, nonlinear programming, integer programming, and heuristic programming, with an emphasis on model building using Excel's freely available Solver. The focus on model building (rather than algorithms) and on spreadsheets makes this book distinctive in this area.

Linear Programming and Network Flows

Author: Mokhtar S. Bazaraa,John J. Jarvis,Hanif D. Sherali

Publisher: John Wiley & Sons

ISBN: 1118211324

Category: Mathematics

Page: 768

View: 1656

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The authoritative guide to modeling and solving complex problemswith linear programming—extensively revised, expanded, andupdated The only book to treat both linear programming techniques andnetwork flows under one cover, Linear Programming and NetworkFlows, Fourth Edition has been completely updated with thelatest developments on the topic. This new edition continues tosuccessfully emphasize modeling concepts, the design and analysisof algorithms, and implementation strategies for problems in avariety of fields, including industrial engineering, managementscience, operations research, computer science, andmathematics. The book begins with basic results on linear algebra and convexanalysis, and a geometrically motivated study of the structure ofpolyhedral sets is provided. Subsequent chapters include coverageof cycling in the simplex method, interior point methods, andsensitivity and parametric analysis. Newly added topics in theFourth Edition include: The cycling phenomenon in linear programming and the geometry ofcycling Duality relationships with cycling Elaboration on stable factorizations and implementationstrategies Stabilized column generation and acceleration of Benders andDantzig-Wolfe decomposition methods Line search and dual ascent ideas for the out-of-kilteralgorithm Heap implementation comments, negative cost circuit insights,and additional convergence analyses for shortest path problems The authors present concepts and techniques that are illustratedby numerical examples along with insights complete with detailedmathematical analysis and justification. An emphasis is placed onproviding geometric viewpoints and economic interpretations as wellas strengthening the understanding of the fundamental ideas. Eachchapter is accompanied by Notes and Referencessections that provide historical developments in addition tocurrent and future trends. Updated exercises allow readers to testtheir comprehension of the presented material, and extensivereferences provide resources for further study. Linear Programming and Network Flows, Fourth Edition isan excellent book for linear programming and network flow coursesat the upper-undergraduate and graduate levels. It is also avaluable resource for applied scientists who would like to refreshtheir understanding of linear programming and network flowtechniques.

Operations Research

Einführung

Author: Frederick S. Hillier,Gerald J. Liebermann

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3486792083

Category: Business & Economics

Page: 868

View: 6259

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Aus dem Inhalt: Was ist Operations Research? Überblick über die Modellierungsgrundsätze des Operations Research. Einführung in die lineare Programmierung. Die Lösung linearer Programmierungsprobleme: Das Simplexverfahren. Stochastische Prozesse. Warteschlangentheorie. Lagerhaltungstheorie. Prognoseverfahren. Markov-Entscheidungsprozesse. Reliabilität. Entscheidungstheorie. Die Theorie des Simplexverfahrens Qualitätstheorie und Sensitivitätsanalyse Spezialfälle linearer Programmierungsprobleme. Die Formulierung linearer Programmierungsmodelle und Goal-Programmierung. Weitere Algorithmen der linearen Programmierung. Netzwerkanalyse einschließlich PERT-CPM. Dynamische Optimierung. Spieltheorie. Ganzzahlige Programmierung. Nichtlineare Programmierung Simulation. Anhang. Lösungen für ausgewählte Übungsaufgaben.

Optimization Methods in Operations Research and Systems Analysis

Author: K V Mital

Publisher: New Age International

ISBN: 9788122408737

Category: Linear programming

Page: 385

View: 6008

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The Mathematical Aspects Of Operations Research And Systems Analysis Concerned With Optimization Of Objectives Form The Subject Of This Book. In Its Revised, Updated And Enlarged Third Edition, Discussion On Linear Programming Has Been Expanded And Recast With Greater Emphasis On Duality Theory, Sensitivity Analysis, Parametric Programming, Multiobjective And Goal Programming And Formulation And Solution Of Practical Problems. Chapters On Nonlinear Programming Include Integer Programming, Kuhn-Tucker Theory, Separable And Quadratic Programming, Dynamic Programming, Geometric Programming And Direct Search And Gradient Methods. A Chapter On Theory Of Games Is Also Included. A Short Note On Karmarkars Projective Algorithm Is Given In The Appendix.The Book Keeps In View The Needs Of The Student Taking A Regular Course In Operations Research Or Mathematical Programming, And Also Of Research Scholars In Other Disciplines Who Have A Limited Objective Of Learning The Practical Aspects Of Various Optimization Methods To Solve Their Special Problems. For The Former, Illustrative Solved Examples And Unsolved Examples At The End Of Each Chapter, Small Enough To Be Solved By Hand, Would Be Of Greater Interest, While For He Latter, Summaries Of Computational Algorithms For Various Methods Which Would Help Him To Write Computer Programmes To Solve Larger Problems Would Be More Helpful. A Few Computer Programmes In Fortran Iv Have Also Been Given In The Appendix.

Finite-Elemente-Methoden

Author: Klaus-Jürgen Bathe

Publisher: Springer Verlag

ISBN: 9783540668060

Category: Technology & Engineering

Page: 1253

View: 1774

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Dieses Lehr- und Handbuch behandelt sowohl die elementaren Konzepte als auch die fortgeschrittenen und zukunftsweisenden linearen und nichtlinearen FE-Methoden in Statik, Dynamik, Festkörper- und Fluidmechanik. Es wird sowohl der physikalische als auch der mathematische Hintergrund der Prozeduren ausführlich und verständlich beschrieben. Das Werk enthält eine Vielzahl von ausgearbeiteten Beispielen, Rechnerübungen und Programmlisten. Als Übersetzung eines erfolgreichen amerikanischen Lehrbuchs hat es sich in zwei Auflagen auch bei den deutschsprachigen Ingenieuren etabliert. Die umfangreichen Änderungen gegenüber der Vorauflage innerhalb aller Kapitel - vor allem aber der fortgeschrittenen - spiegeln die rasche Entwicklung innerhalb des letzten Jahrzehnts auf diesem Gebiet wieder.

Transactions

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Insurance, LIfe

Page: N.A

View: 1193

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Beginning with vol. for 1951 includes section: Reports of mortality and morbidity experience.

Nonlinear Programming

Sequential Unconstrained Minimization Techniques

Author: Anthony V. Fiacco,Garth P. McCormick

Publisher: SIAM

ISBN: 0898712548

Category: Mathematics

Page: 210

View: 5892

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Analyzes the 'central' or 'dual' trajectory used by modern path following and primal/dual methods for convex / general linear programming.

Nonlinear programming

theory and algorithms

Author: M. S. Bazaraa,C. M. Shetty

Publisher: John Wiley & Sons

ISBN: N.A

Category: Mathematics

Page: 560

View: 7686

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Convex analysis; convex sets; convex functions; optimality conditions and duality; the Fritz John and Kuhn-Tucker optimality conditions; constraint qualifications; lagrangian duality and saddle point optimality conditions; algorithms and their convergence; the concept of an algorithm; unconstrained optimization; penalty and Barrier functions; methods of feasible directions; linear complementarity, and quadratic, separable, and fractional programming; mathematical review; summary of convexity, optimality conditions, and duality.

Quasi-Newton Methods for Nonlinear Programming

Author: Jason Dean Hibbeler,University of Illinois at Urbana-Champaign. Department of Computer Science

Publisher: N.A

ISBN: N.A

Category: Differential equations, Nonlinear

Page: 220

View: 2447

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Abstract: "In this thesis, we examine nonlinear programming from the standpoint of nonlinear equations. We consider Newton and quasi-Newton algorithms for solving underdetermined nonlinear systems and then show how these techniques can be applied in the setting of constrained optimization. We produce new perturbation analyses for the special symmetric block system resulting from a standard solution method in nonlinear programming. Using the steepest descent method for unconstrained optimization, we develop a new iteration for the constrained case. We give a convergence analysis for this new method and illustrate its behavior with numerical examples. Finally, we propose a new class of symmetric updates for use in a quasi-Newton method for nonlinear programming. We show how these updates model the underlying nonlinear equation better than the standard symmetric updates and also how they require less overall work for large problems."