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This book provides practitioners as well as students of this general methodology with an easily accessible introduction to the new class of algorithms known as interior-point methods for linear programming.
The era of interior point methods (IPMs) was initiated by N. Karmarkar’s 1984 paper, which triggered turbulent research and reshaped almost all areas of optimization theory and computational practice. This book offers comprehensive coverage of IPMs. It details the main results of more than a decade of IPM research. Numerous exercises are provided to aid in understanding the material.
The approach to LO in this book is new in many aspects. In particular the IPM based development of duality theory is surprisingly elegant. The algorithmic parts of the book contain a complete discussion of many algorithmic variants, including predictor-corrector methods, partial updating, higher order methods and sensitivity and parametric analysis.
In the past decade, primal-dual algorithms have emerged as the most important and useful algorithms from the interior-point class. This book presents the major primal-dual algorithms for linear programming in straightforward terms. A thorough description of the theoretical properties of these methods is given, as are a discussion of practical and computational aspects and a summary of current software. This is an excellent, timely, and well-written work. The major primal-dual algorithms covered in this book are path-following algorithms (short- and long-step, predictor-corrector), potential-reduction algorithms, and infeasible-interior-point algorithms. A unified treatment of superlinear convergence, finite termination, and detection of infeasible problems is presented. Issues relevant to practical implementation are also discussed, including sparse linear algebra and a complete specification of Mehrotra's predictor-corrector algorithm. Also treated are extensions of primal-dual algorithms to more general problems such as monotone complementarity, semidefinite programming, and general convex programming problems.
The first comprehensive review of the theory and practice of one oftoday's most powerful optimization techniques. The explosive growth of research into and development of interiorpoint algorithms over the past two decades has significantlyimproved the complexity of linear programming and yielded some oftoday's most sophisticated computing techniques. This book offers acomprehensive and thorough treatment of the theory, analysis, andimplementation of this powerful computational tool. Interior Point Algorithms provides detailed coverage of all basicand advanced aspects of the subject. Beginning with an overview offundamental mathematical procedures, Professor Yinyu Ye movesswiftly on to in-depth explorations of numerous computationalproblems and the algorithms that have been developed to solve them.An indispensable text/reference for students and researchers inapplied mathematics, computer science, operations research,management science, and engineering, Interior Point Algorithms: * Derives various complexity results for linear and convexprogramming * Emphasizes interior point geometry and potential theory * Covers state-of-the-art results for extension, implementation,and other cutting-edge computational techniques * Explores the hottest new research topics, including nonlinearprogramming and nonconvex optimization.
Here is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming. The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design. The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book's focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide spectrum of important optimization problems arising in applications.
This book presents a structured approach to formulate, model, and solve mathematical optimization problems for a wide range of real world situations. Among the problems covered are production, distribution and supply chain planning, scheduling, vehicle routing, as well as cutting stock, packing, and nesting. The optimization techniques used to solve the problems are primarily linear, mixed-integer linear, nonlinear, and mixed integer nonlinear programming. The book also covers important considerations for solving real-world optimization problems, such as dealing with valid inequalities and symmetry during the modeling phase, but also data interfacing and visualization of results in a more and more digitized world. The broad range of ideas and approaches presented helps the reader to learn how to model a variety of problems from process industry, paper and metals industry, the energy sector, and logistics using mathematical optimization techniques.
Students with diverse backgrounds will face a multitude of decisions in a variety of engineering, scientific, industrial, and financial settings. They will need to know how to identify problems that the methods of operations research (OR) can solve, how to structure the problems into standard mathematical models, and finally how to apply or develop computational tools to solve the problems. Perfect for any one-semester course in OR, Operations Research: A Practical Introduction answers all of these needs. In addition to providing a practical introduction and guide to using OR techniques, it includes a timely examination of innovative methods and practical issues related to the development and use of computer implementations. It provides a sound introduction to the mathematical models relevant to OR and illustrates the effective use of OR techniques with examples drawn from industrial, computing, engineering, and business applications. Many students will take only one course in the techniques of Operations Research. Operations Research: A Practical Introduction offers them the greatest benefit from that course through a broad survey of the techniques and tools available for quantitative decision making. It will also encourage other students to pursue more advanced studies and provides you a concise, well-structured, vehicle for delivering the best possible overview of the discipline.
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.
Aimed at final year undergraduate students, this is the first volume to publish in a new series of text covering core subjects in operational research in an accessible student-friendly format. This volume presents simulation paired with inventory control. The Operational Research Series aims to provide a new generation of European-originated texts of practical relevance to todays student. To guarantee accessibility, the texts are concise and have a non-mathematical orientation. These texts will provide students with the grounding in operational research theory they need to become the innovators of tomorrow. This is one of the first volumes in a new series of textbooks in operational research. The key objectives of the series are to provide concise introductions to the core topics in operational research focusing on the practical relevance of those topics to today's students and taking a non-mathematical orientation in favour of software applications. Each core subject will be paired with another core subject in order to provide maximum value for money for students.