The primary goal of this book is to provide a self-contained, comprehensive study of the main first-order methods that are frequently used in solving large-scale problems. First-order methods exploit information on val...
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ISBN:
(数字)9781611974997
ISBN:
(纸本)9781611974980
The primary goal of this book is to provide a self-contained, comprehensive study of the main first-order methods that are frequently used in solving large-scale problems. First-order methods exploit information on values and gradients/subgradients (but not Hessians) of the functions composing the model under consideration. With the increase in the number of applications that can be modeled as large or even huge-scale optimization problems, there has been a revived interest in using simple methods that require low iteration cost as well as low memory *** author has gathered, reorganized, and synthesized (in a unified manner) many results that are currently scattered throughout the literature, many of which cannot be typically found in optimization ***-Order Methods in optimization offers comprehensive study of first-order methods with the theoretical foundations; provides plentiful examples and illustrations; emphasizes rates of convergence and complexity analysis of the main first-order methods used to solve large-scale problems; and covers both variables and functional decomposition ***: This book is intended primarily for researchers and graduate students in mathematics, computer sciences, and electrical and other engineering departments. Readers with a background in advanced calculus and linear algebra, as well as prior knowledge in the fundamentals of optimization (some convex analysis, optimality conditions, and duality), will be best prepared for the material.
This book addresses a seemingly simple question: Can a certain amount of gas be transported within a pipeline network? The question is difficult, however, when asked in relation to a meshed nationwide gas transportati...
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ISBN:
(数字)9781611973693
ISBN:
(纸本)9781611973686
This book addresses a seemingly simple question: Can a certain amount of gas be transported within a pipeline network? The question is difficult, however, when asked in relation to a meshed nationwide gas transportation network and when taking into account technical details and discrete decisions, as well as regulations, contracts, and varying demands involved. This book provides an introduction to the field of gas transportation planning and discusses in detail the advantages and disadvantages of several mathematical models that address gas transport within the context of the technical and regulatory framework. It shows how to solve the models using sophisticated mathematical optimization algorithms and includes examples of large-scale applications of mathematical optimization to this real-world industrial problem.
This book provides a thorough and up-to-date discussion of arc routing by world-renowned researchers. Organized by problem type, the book offers a rigorous treatment of complexity issues, models, algorithms, and appli...
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ISBN:
(数字)9781611973679
ISBN:
(纸本)9781611973662
This book provides a thorough and up-to-date discussion of arc routing by world-renowned researchers. Organized by problem type, the book offers a rigorous treatment of complexity issues, models, algorithms, and applications.
Arc Routing: Problems, Methods, and Applications opens with a historical perspective of the field and is followed by three sections that cover complexity and the Chinese Postman and the Rural Postman problems, the Capacitated Arc Routing Problem and routing problems with min-max and profit maximization objectives, and important applications, including meter reading, snow removal, and waste collection.
The power grid can be considered one of twentieth-century engineering's greatest achievements, and as grids and populations grow, robustness is a factor that planners must take into account. Power grid robustness ...
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ISBN:
(数字)9781611974164
ISBN:
(纸本)9781611974157
The power grid can be considered one of twentieth-century engineering's greatest achievements, and as grids and populations grow, robustness is a factor that planners must take into account. Power grid robustness is a complex problem for two reasons: the underlying physics is mathematically complex, and modeling is complicated by lack of accurate data.
This book sheds light on this complex problem by
introducing the engineering details of power grid operations from the basic to the detailed;
describing how to use optimization and stochastic modeling, with special focus on the modeling of cascading failures and robustness;
providing numerical examples that show “how things work”; and
detailing the application of a number of optimization theories to power grids.
Vehicle routing problems, among the most studied in combinatorial optimization, arise in many practical contexts (freight distribution and collection, transportation, garbage collection, newspaper delivery, etc.). Ope...
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ISBN:
(数字)9781611973594
ISBN:
(纸本)9781611973587
Vehicle routing problems, among the most studied in combinatorial optimization, arise in many practical contexts (freight distribution and collection, transportation, garbage collection, newspaper delivery, etc.). Operations researchers have made significant developments in the algorithms for their solution, and Vehicle Routing: Problems, Methods, and Applications, Second Edition reflects these advances. The text of the new edition is either completely new or significantly revised and
provides extensive and complete state-of-the-art coverage of vehicle routing by those who have done most of the innovative research in the area;
emphasizes methodology related to specific classes of vehicle routing problems and, since vehicle routing is used as a benchmark for all new solution techniques, contains a complete overview of current solutions to combinatorial optimization problems;
includes several chapters on important and emerging applications, such as disaster relief and green vehicle routing.
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