nonlinear programming theory and algorithms

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Nonlinear Programming

Author : Mokhtar S. Bazaraa
ISBN : 9781118626306
Genre : Mathematics
File Size : 48. 25 MB
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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.

Nonlinear Programming

Author : M. S. Bazaraa
ISBN : UOM:39015047426682
Genre : Mathematics
File Size : 53. 6 MB
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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.

Solutions Manual To Accompany Nonlinear Programming

Author : Mokhtar S. Bazaraa
ISBN : 9781118762325
Genre : Mathematics
File Size : 78. 50 MB
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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.

Introduction To Nonlinear Optimization

Author : Amir Beck
ISBN : 9781611973648
Genre : Mathematics
File Size : 71. 69 MB
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This book provides the foundations of the theory of nonlinear optimization as well as some related algorithms and presents a variety of applications from diverse areas of applied sciences. The author combines three pillars of optimization?theoretical and algorithmic foundation, familiarity with various applications, and the ability to apply the theory and algorithms on actual problems?and rigorously and gradually builds the connection between theory, algorithms, applications, and implementation. Readers will find more than 170 theoretical, algorithmic, and numerical exercises that deepen and enhance the reader's understanding of the topics. The author includes offers several subjects not typically found in optimization books?for example, optimality conditions in sparsity-constrained optimization, hidden convexity, and total least squares. The book also offers a large number of applications discussed theoretically and algorithmically, such as circle fitting, Chebyshev center, the Fermat?Weber problem, denoising, clustering, total least squares, and orthogonal regression and theoretical and algorithmic topics demonstrated by the MATLAB? toolbox CVX and a package of m-files that is posted on the book?s web site.

Mathematical Programming

Author : Michel Minoux
ISBN : 0471901709
Genre : Mathematics
File Size : 71. 81 MB
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Nonlinear Programming

Author : Garth P. McCormick
ISBN : 0471093092
Genre : Mathematics
File Size : 40. 20 MB
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A comprehensive, high-level introduction to the theoretical, computational, and modelling aspects of practical nonlinear programming and optimization. Provides an exposition of algorithms for solving NLP and optimization problems. Presents case studies and optimization models of real-world problems. Introduces mathematical analysis, convexity, and linear algebra fundamentals. Presents ``factorable'' functions to provide interface between computer coded algorithms and the algebraic representation of nonlinear programming problems. Includes exercises.

Linear And Nonlinear Optimization

Author : Igor Griva
ISBN : 9780898717730
Genre : Linear programming
File Size : 39. 94 MB
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Provides an introduction to the applications, theory, and algorithms of linear and nonlinear optimization. The emphasis is on practical aspects - discussing modern algorithms, as well as the influence of theory on the interpretation of solutions or on the design of software. The book includes several examples of realistic optimization models that address important applications. The succinct style of this second edition is punctuated with numerous real-life examples and exercises, and the authors include accessible explanations of topics that are not often mentioned in textbooks, such as duality in nonlinear optimization, primal-dual methods for nonlinear optimization, filter methods, and applications such as support-vector machines. The book is designed to be flexible. It has a modular structure, and uses consistent notation and terminology throughout. It can be used in many different ways, in many different courses, and at many different levels of sophistication.

Nonlinear Programming For Operations Research

Author : Donald M. Simmons
ISBN : UOM:39015009816987
Genre : Mathematics
File Size : 64. 98 MB
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Introduction to nonlinear programming; Review of linear programming; Further mathematical background; Classical uncostrained optimization; Optimum-seeking by experimentation; Lagrange multipliers and kuhn-tucker theory; Quadratic programming; Algorithms for linearly constrained problems; Algorithms for nonlinear constrained problems.

High Performance Algorithms And Software For Nonlinear Optimization

Author : Gianni Pillo
ISBN : 9781461302414
Genre : Mathematics
File Size : 36. 86 MB
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This volume contains the edited texts of the lectures presented at the Workshop on High Performance Algorithms and Software for Nonlinear Optimization held in Erice, Sicily, at the "G. Stampacchia" School of Mathematics of the "E. Majorana" Centre for Scientific Culture, June 30 - July 8, 2001. In the first year of the new century, the aim of the Workshop was to assess the past and to discuss the future of Nonlinear Optimization, and to highlight recent achieve ments and promising research trends in this field. An emphasis was requested on algorithmic and high performance software developments and on new computational experiences, as well as on theoretical advances. We believe that such goal was basically achieved. The Workshop was attended by 71 people from 22 countries. Although not all topics were covered, the presentations gave indeed a wide overview of the field, from different and complementary stand points. Besides the lectures, several formal and informal discussions took place. We wish to express our appreciation for the active contribution of all the participants in the meeting. The 18 papers included in this volume represent a significant selection of the most recent developments in nonlinear programming theory and practice. They show that there is plenty of exciting ideas, implementation issues and new applications which produce a very fast evolution in the field.

Linear Programming And Network Flows

Author : Mokhtar S. Bazaraa
ISBN : 9781118211328
Genre : Mathematics
File Size : 38. 25 MB
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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.

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