Quasi-Newton Methods Converge at the Golden Rate PDF Download
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Author: J. Barzilai
Publisher:
ISBN:
Category : Algorithms
Languages : en
Pages : 10
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Book Description
Author: J. Barzilai
Publisher:
ISBN:
Category : Algorithms
Languages : en
Pages : 10
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Book Description
Author: J. Barzilai
Publisher:
ISBN:
Category : Convergence
Languages : en
Pages : 13
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Book Description
We prove that the rate of convergence of quasi-Newton methods is the golden section ratio (1 + square root of 5)/2. (Author).
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 952
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Book Description
Author:
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 174
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Book Description
Author: William H. Press
Publisher: Cambridge University Press
ISBN: 9780521884075
Category : Mathematics
Languages : en
Pages : 1272
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Book Description
The complete Numerical Recipes 3rd edition book/CD bundle, with a hundred new routines, two new chapters and much more.
Author: Elijah Polak
Publisher: Springer Science & Business Media
ISBN: 1461206634
Category : Mathematics
Languages : en
Pages : 801
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Book Description
This book deals with optimality conditions, algorithms, and discretization tech niques for nonlinear programming, semi-infinite optimization, and optimal con trol problems. The unifying thread in the presentation consists of an abstract theory, within which optimality conditions are expressed in the form of zeros of optimality junctions, algorithms are characterized by point-to-set iteration maps, and all the numerical approximations required in the solution of semi-infinite optimization and optimal control problems are treated within the context of con sistent approximations and algorithm implementation techniques. Traditionally, necessary optimality conditions for optimization problems are presented in Lagrange, F. John, or Karush-Kuhn-Tucker multiplier forms, with gradients used for smooth problems and subgradients for nonsmooth prob lems. We present these classical optimality conditions and show that they are satisfied at a point if and only if this point is a zero of an upper semicontinuous optimality junction. The use of optimality functions has several advantages. First, optimality functions can be used in an abstract study of optimization algo rithms. Second, many optimization algorithms can be shown to use search directions that are obtained in evaluating optimality functions, thus establishing a clear relationship between optimality conditions and algorithms. Third, estab lishing optimality conditions for highly complex problems, such as optimal con trol problems with control and trajectory constraints, is much easier in terms of optimality functions than in the classical manner. In addition, the relationship between optimality conditions for finite-dimensional problems and semi-infinite optimization and optimal control problems becomes transparent.
Author: Sergiy Butenko
Publisher: CRC Press
ISBN: 1466577770
Category : Business & Economics
Languages : en
Pages : 415
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Book Description
For students in industrial and systems engineering (ISE) and operations research (OR) to understand optimization at an advanced level, they must first grasp the analysis of algorithms, computational complexity, and other concepts and modern developments in numerical methods. Satisfying this prerequisite, Numerical Methods and Optimization: An Introduction combines the materials from introductory numerical methods and introductory optimization courses into a single text. This classroom-tested approach enriches a standard numerical methods syllabus with optional chapters on numerical optimization and provides a valuable numerical methods background for students taking an introductory OR or optimization course. The first part of the text introduces the necessary mathematical background, the digital representation of numbers, and different types of errors associated with numerical methods. The second part explains how to solve typical problems using numerical methods. Focusing on optimization methods, the final part presents basic theory and algorithms for linear and nonlinear optimization. The book assumes minimal prior knowledge of the topics. Taking a rigorous yet accessible approach to the material, it includes some mathematical proofs as samples of rigorous analysis but in most cases, uses only examples to illustrate the concepts. While the authors provide a MATLAB® guide and code available for download, the book can be used with other software packages.
Author: E. Polak
Publisher: Academic Press
ISBN: 008096091X
Category : Business & Economics
Languages : en
Pages : 351
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Book Description
Computational Methods in Optimization
Author: Igor Griva
Publisher: SIAM
ISBN: 0898717736
Category : Mathematics
Languages : en
Pages : 743
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Book Description
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.
Author: Larry W. Mays
Publisher: Water Resources Publication
ISBN: 9781887201322
Category : Business & Economics
Languages : en
Pages : 550
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Book Description
This book is intended to be a textbook for students of water resources engineering and management. It is an introduction to methods used in hydrosystems for upper level undergraduate and graduate students. The material can be presented to students with no background in operations research and with only an undergraduate background in hydrology and hydraulics. A major focus is to bring together the use of economics, operations research, probability and statistics with the use of hydrology, hydraulics, and water resources for the analysis, design, operation, and management of various types of water projects. This book is an excellent reference for engineers, water resource planners, water resource systems analysts, and water managers. This book is concerned with the mathematical modeling of problems in water project design, analysis, operation, and management. The quantitative methods include: (a) the simulation of various hydrologic and hydraulic processes; (b) the use of operations research, probability and statistics, and economics. Rarely have these methods been integrated in a systematic framework in a single book like Hydrosystems Engineering and Management. An extensive number of example problems are presented for ease in understanding the material. In addition, a large number of end-of-chapter problems are provided for use in homework assignments.
