The Mathematics of Nonlinear Programming PDF Download
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Author: Anthony L. Peressini
Publisher: Springer
ISBN: 9781461269892
Category : Mathematics
Languages : en
Pages : 0
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Book Description
Nonlinear programming provides an excellent opportunity to explore an interesting variety of pure and solidly applicable mathematics, numerical analysis, and computing. This text develops some of the ideas and techniques involved in the optimization methods using calculus, leading to the study of convexity. This is followed by material on basic numerical methods, least squares, the Karush-Kuhn-Tucker theorem, penalty functions, and Lagrange multipliers. The authors have aimed their presentation at the student who has a working knowledge of matrix algebra and advanced calculus, but has had no previous exposure to optimization.
Author: Anthony L. Peressini
Publisher: Springer
ISBN: 9781461269892
Category : Mathematics
Languages : en
Pages : 0
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Book Description
Nonlinear programming provides an excellent opportunity to explore an interesting variety of pure and solidly applicable mathematics, numerical analysis, and computing. This text develops some of the ideas and techniques involved in the optimization methods using calculus, leading to the study of convexity. This is followed by material on basic numerical methods, least squares, the Karush-Kuhn-Tucker theorem, penalty functions, and Lagrange multipliers. The authors have aimed their presentation at the student who has a working knowledge of matrix algebra and advanced calculus, but has had no previous exposure to optimization.
Author: Lorenz T. Biegler
Publisher: SIAM
ISBN: 0898719380
Category : Science
Languages : en
Pages : 411
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Book Description
This book addresses modern nonlinear programming (NLP) concepts and algorithms, especially as they apply to challenging applications in chemical process engineering. The author provides a firm grounding in fundamental NLP properties and algorithms, and relates them to real-world problem classes in process optimization, thus making the material understandable and useful to chemical engineers and experts in mathematical optimization.
Author: Mokhtar S. Bazaraa
Publisher: John Wiley & Sons
ISBN: 1118626303
Category : Mathematics
Languages : en
Pages : 867
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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: Jon Lee
Publisher: Springer Science & Business Media
ISBN: 1461419271
Category : Mathematics
Languages : en
Pages : 692
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Book Description
Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions. Mixed-integer nonlinear programming (MINLP) problems combine the numerical difficulties of handling nonlinear functions with the challenge of optimizing in the context of nonconvex functions and discrete variables. MINLP is one of the most flexible modeling paradigms available for optimization; but because its scope is so broad, in the most general cases it is hopelessly intractable. Nonetheless, an expanding body of researchers and practitioners — including chemical engineers, operations researchers, industrial engineers, mechanical engineers, economists, statisticians, computer scientists, operations managers, and mathematical programmers — are interested in solving large-scale MINLP instances.
Author: Andrzej Ruszczynski
Publisher: Princeton University Press
ISBN: 1400841054
Category : Mathematics
Languages : en
Pages : 464
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Book Description
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern topics such as optimality conditions and numerical methods for problems involving nondifferentiable functions, semidefinite programming, metric regularity and stability theory of set-constrained systems, and sensitivity analysis of optimization problems. Based on a decade's worth of notes the author compiled in successfully teaching the subject, this book will help readers to understand the mathematical foundations of the modern theory and methods of nonlinear optimization and to analyze new problems, develop optimality theory for them, and choose or construct numerical solution methods. It is a must for anyone seriously interested in optimization.
Author: Paul E. Fishback
Publisher: CRC Press
ISBN: 9781420090659
Category : Business & Economics
Languages : en
Pages : 413
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Book Description
Helps Students Understand Mathematical Programming Principles and Solve Real-World Applications Supplies enough mathematical rigor yet accessible enough for undergraduates Integrating a hands-on learning approach, a strong linear algebra focus, MapleTM software, and real-world applications, Linear and Nonlinear Programming with MapleTM: An Interactive, Applications-Based Approach introduces undergraduate students to the mathematical concepts and principles underlying linear and nonlinear programming. This text fills the gap between management science books lacking mathematical detail and rigor and graduate-level books on mathematical programming. Essential linear algebra tools Throughout the text, topics from a first linear algebra course, such as the invertible matrix theorem, linear independence, transpose properties, and eigenvalues, play a prominent role in the discussion. The book emphasizes partitioned matrices and uses them to describe the simplex algorithm in terms of matrix multiplication. This perspective leads to streamlined approaches for constructing the revised simplex method, developing duality theory, and approaching the process of sensitivity analysis. The book also discusses some intermediate linear algebra topics, including the spectral theorem and matrix norms. Maple enhances conceptual understanding and helps tackle problems Assuming no prior experience with Maple, the author provides a sufficient amount of instruction for students unfamiliar with the software. He also includes a summary of Maple commands as well as Maple worksheets in the text and online. By using Maple’s symbolic computing components, numeric capabilities, graphical versatility, and intuitive programming structures, students will acquire a deep conceptual understanding of major mathematical programming principles, along with the ability to solve moderately sized real-world applications. Hands-on activities that engage students Throughout the book, student understanding is evaluated through "waypoints" that involve basic computations or short questions. Some problems require paper-and-pencil calculations; others involve more lengthy calculations better suited for performing with Maple. Many sections contain exercises that are conceptual in nature and/or involve writing proofs. In addition, six substantial projects in one of the appendices enable students to solve challenging real-world problems.
Author: Dimitri P. Bertsekas
Publisher: Goodman Publishers
ISBN:
Category : Mathematics
Languages : en
Pages : 806
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Book Description
Author: Jonathan Borwein
Publisher: Springer Science & Business Media
ISBN: 0387312560
Category : Mathematics
Languages : en
Pages : 316
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Book Description
Optimization is a rich and thriving mathematical discipline, and the underlying theory of current computational optimization techniques grows ever more sophisticated. This book aims to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. Each section concludes with an often extensive set of optional exercises. This new edition adds material on semismooth optimization, as well as several new proofs.
Author: Francisco J. Aragón
Publisher: Springer
ISBN: 3030111849
Category : Mathematics
Languages : en
Pages : 350
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Book Description
This textbook on nonlinear optimization focuses on model building, real world problems, and applications of optimization models to natural and social sciences. Organized into two parts, this book may be used as a primary text for courses on convex optimization and non-convex optimization. Definitions, proofs, and numerical methods are well illustrated and all chapters contain compelling exercises. The exercises emphasize fundamental theoretical results on optimality and duality theorems, numerical methods with or without constraints, and derivative-free optimization. Selected solutions are given. Applications to theoretical results and numerical methods are highlighted to help students comprehend methods and techniques.
Author: Olvi L. Mangasarian
Publisher: SIAM
ISBN: 0898713412
Category : Mathematics
Languages : en
Pages : 231
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Book Description
This reprint of the 1969 book of the same name is a concise, rigorous, yet accessible, account of the fundamentals of constrained optimization theory. Many problems arising in diverse fields such as machine learning, medicine, chemical engineering, structural design, and airline scheduling can be reduced to a constrained optimization problem. This book provides readers with the fundamentals needed to study and solve such problems. Beginning with a chapter on linear inequalities and theorems of the alternative, basics of convex sets and separation theorems are then derived based on these theorems. This is followed by a chapter on convex functions that includes theorems of the alternative for such functions. These results are used in obtaining the saddlepoint optimality conditions of nonlinear programming without differentiability assumptions.
