Optimization And Differentiation

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Automatic Differentiation of Algorithms

Author : George Corliss
Publisher : Springer Science & Business Media
ISBN 13 : 1461300754
Total Pages : 431 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Automatic Differentiation of Algorithms by : George Corliss

Download or read book Automatic Differentiation of Algorithms written by George Corliss and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey book focusing on the key relationships and synergies between automatic differentiation (AD) tools and other software tools, such as compilers and parallelizers, as well as their applications. The key objective is to survey the field and present the recent developments. In doing so the topics covered shed light on a variety of perspectives. They reflect the mathematical aspects, such as the differentiation of iterative processes, and the analysis of nonsmooth code. They cover the scientific programming aspects, such as the use of adjoints in optimization and the propagation of rounding errors. They also cover "implementation" problems.

Optimization and Differentiation

Author : Simon Serovajsky
Publisher : CRC Press
ISBN 13 : 1351648489
Total Pages : 587 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis Optimization and Differentiation by : Simon Serovajsky

Download or read book Optimization and Differentiation written by Simon Serovajsky and published by CRC Press. This book was released on 2017-09-13 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization and Differentiation is an introduction to the application of optimization control theory to systems described by nonlinear partial differential equations. As well as offering a useful reference work for researchers in these fields, it is also suitable for graduate students of optimal control theory.

Evaluating Derivatives

Author : Andreas Griewank
Publisher : SIAM
ISBN 13 : 0898716594
Total Pages : 448 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Evaluating Derivatives by : Andreas Griewank

Download or read book Evaluating Derivatives written by Andreas Griewank and published by SIAM. This book was released on 2008-11-06 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title is a comprehensive treatment of algorithmic, or automatic, differentiation. The second edition covers recent developments in applications and theory, including an elegant NP completeness argument and an introduction to scarcity.

Variational Methods in Optimization

Author : Donald R. Smith
Publisher : Courier Corporation
ISBN 13 : 9780486404554
Total Pages : 406 pages
Book Rating : 4.4/5 (45 download)

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Book Synopsis Variational Methods in Optimization by : Donald R. Smith

Download or read book Variational Methods in Optimization written by Donald R. Smith and published by Courier Corporation. This book was released on 1998-01-01 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Highly readable text elucidates applications of the chain rule of differentiation, integration by parts, parametric curves, line integrals, double integrals, and elementary differential equations. 1974 edition.

Optimization and Differentiation

Author : Simon Serovajsky
Publisher : CRC Press
ISBN 13 : 1498750958
Total Pages : 539 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Optimization and Differentiation by : Simon Serovajsky

Download or read book Optimization and Differentiation written by Simon Serovajsky and published by CRC Press. This book was released on 2017-09-13 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization and Differentiation is an introduction to the application of optimization control theory to systems described by nonlinear partial differential equations. As well as offering a useful reference work for researchers in these fields, it is also suitable for graduate students of optimal control theory.

Large-Scale PDE-Constrained Optimization

Author : Lorenz T. Biegler
Publisher : Springer Science & Business Media
ISBN 13 : 364255508X
Total Pages : 347 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Large-Scale PDE-Constrained Optimization by : Lorenz T. Biegler

Download or read book Large-Scale PDE-Constrained Optimization written by Lorenz T. Biegler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal design, optimal control, and parameter estimation of systems governed by partial differential equations (PDEs) give rise to a class of problems known as PDE-constrained optimization. The size and complexity of the discretized PDEs often pose significant challenges for contemporary optimization methods. With the maturing of technology for PDE simulation, interest has now increased in PDE-based optimization. The chapters in this volume collectively assess the state of the art in PDE-constrained optimization, identify challenges to optimization presented by modern highly parallel PDE simulation codes, and discuss promising algorithmic and software approaches for addressing them. These contributions represent current research of two strong scientific computing communities, in optimization and PDE simulation. This volume merges perspectives in these two different areas and identifies interesting open questions for further research.

Variational Analysis and Generalized Differentiation in Optimization and Control

Author : Regina S. Burachik
Publisher : Springer Science & Business Media
ISBN 13 : 1441904379
Total Pages : 237 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Variational Analysis and Generalized Differentiation in Optimization and Control by : Regina S. Burachik

Download or read book Variational Analysis and Generalized Differentiation in Optimization and Control written by Regina S. Burachik and published by Springer Science & Business Media. This book was released on 2010-11-25 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents some 20 papers describing recent developments in advanced variational analysis, optimization, and control systems, especially those based on modern variational techniques and tools of generalized differentiation.

Optimization for Machine Learning

Author : Suvrit Sra
Publisher : MIT Press
ISBN 13 : 026201646X
Total Pages : 509 pages
Book Rating : 4.2/5 (62 download)

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Book Synopsis Optimization for Machine Learning by : Suvrit Sra

Download or read book Optimization for Machine Learning written by Suvrit Sra and published by MIT Press. This book was released on 2012 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date account of the interplay between optimization and machine learning, accessible to students and researchers in both communities. The interplay between optimization and machine learning is one of the most important developments in modern computational science. Optimization formulations and methods are proving to be vital in designing algorithms to extract essential knowledge from huge volumes of data. Machine learning, however, is not simply a consumer of optimization technology but a rapidly evolving field that is itself generating new optimization ideas. This book captures the state of the art of the interaction between optimization and machine learning in a way that is accessible to researchers in both fields. Optimization approaches have enjoyed prominence in machine learning because of their wide applicability and attractive theoretical properties. The increasing complexity, size, and variety of today's machine learning models call for the reassessment of existing assumptions. This book starts the process of reassessment. It describes the resurgence in novel contexts of established frameworks such as first-order methods, stochastic approximations, convex relaxations, interior-point methods, and proximal methods. It also devotes attention to newer themes such as regularized optimization, robust optimization, gradient and subgradient methods, splitting techniques, and second-order methods. Many of these techniques draw inspiration from other fields, including operations research, theoretical computer science, and subfields of optimization. The book will enrich the ongoing cross-fertilization between the machine learning community and these other fields, and within the broader optimization community.

Numerical Optimization

Author : Jorge Nocedal
Publisher : Springer Science & Business Media
ISBN 13 : 0387400656
Total Pages : 686 pages
Book Rating : 4.3/5 (874 download)

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Book Synopsis Numerical Optimization by : Jorge Nocedal

Download or read book Numerical Optimization written by Jorge Nocedal and published by Springer Science & Business Media. This book was released on 2006-12-11 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization is an important tool used in decision science and for the analysis of physical systems used in engineering. One can trace its roots to the Calculus of Variations and the work of Euler and Lagrange. This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.

Dynamic Optimization, Second Edition

Author : Morton I. Kamien
Publisher : Courier Corporation
ISBN 13 : 0486310280
Total Pages : 402 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Dynamic Optimization, Second Edition by : Morton I. Kamien

Download or read book Dynamic Optimization, Second Edition written by Morton I. Kamien and published by Courier Corporation. This book was released on 2013-04-17 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition.

A Derivative-free Two Level Random Search Method for Unconstrained Optimization

Author : Neculai Andrei
Publisher : Springer Nature
ISBN 13 : 3030685179
Total Pages : 126 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis A Derivative-free Two Level Random Search Method for Unconstrained Optimization by : Neculai Andrei

Download or read book A Derivative-free Two Level Random Search Method for Unconstrained Optimization written by Neculai Andrei and published by Springer Nature. This book was released on 2021-03-31 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is intended for graduate students and researchers in mathematics, computer science, and operational research. The book presents a new derivative-free optimization method/algorithm based on randomly generated trial points in specified domains and where the best ones are selected at each iteration by using a number of rules. This method is different from many other well established methods presented in the literature and proves to be competitive for solving many unconstrained optimization problems with different structures and complexities, with a relative large number of variables. Intensive numerical experiments with 140 unconstrained optimization problems, with up to 500 variables, have shown that this approach is efficient and robust. Structured into 4 chapters, Chapter 1 is introductory. Chapter 2 is dedicated to presenting a two level derivative-free random search method for unconstrained optimization. It is assumed that the minimizing function is continuous, lower bounded and its minimum value is known. Chapter 3 proves the convergence of the algorithm. In Chapter 4, the numerical performances of the algorithm are shown for solving 140 unconstrained optimization problems, out of which 16 are real applications. This shows that the optimization process has two phases: the reduction phase and the stalling one. Finally, the performances of the algorithm for solving a number of 30 large-scale unconstrained optimization problems up to 500 variables are presented. These numerical results show that this approach based on the two level random search method for unconstrained optimization is able to solve a large diversity of problems with different structures and complexities. There are a number of open problems which refer to the following aspects: the selection of the number of trial or the number of the local trial points, the selection of the bounds of the domains where the trial points and the local trial points are randomly generated and a criterion for initiating the line search.

Advances in Automatic Differentiation

Author : Christian H. Bischof
Publisher : Springer Science & Business Media
ISBN 13 : 3540689427
Total Pages : 366 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Advances in Automatic Differentiation by : Christian H. Bischof

Download or read book Advances in Automatic Differentiation written by Christian H. Bischof and published by Springer Science & Business Media. This book was released on 2008-08-17 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fifth International Conference on Automatic Differentiation held from August 11 to 15, 2008 in Bonn, Germany, is the most recent one in a series that began in Breckenridge, USA, in 1991 and continued in Santa Fe, USA, in 1996, Nice, France, in 2000 and Chicago, USA, in 2004. The 31 papers included in these proceedings re?ect the state of the art in automatic differentiation (AD) with respect to theory, applications, and tool development. Overall, 53 authors from institutions in 9 countries contributed, demonstrating the worldwide acceptance of AD technology in computational science. Recently it was shown that the problem underlying AD is indeed NP-hard, f- mally proving the inherently challenging nature of this technology. So, most likely, no deterministic “silver bullet” polynomial algorithm can be devised that delivers optimum performance for general codes. In this context, the exploitation of doma- speci?c structural information is a driving issue in advancing practical AD tool and algorithm development. This trend is prominently re?ected in many of the pub- cations in this volume, not only in a better understanding of the interplay of AD and certain mathematical paradigms, but in particular in the use of hierarchical AD approaches that judiciously employ general AD techniques in application-speci?c - gorithmic harnesses. In this context, the understanding of structures such as sparsity of derivatives, or generalizations of this concept like scarcity, plays a critical role, in particular for higher derivative computations.

A First Course in Optimization

Author : Charles Byrne
Publisher : CRC Press
ISBN 13 : 1482226588
Total Pages : 313 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis A First Course in Optimization by : Charles Byrne

Download or read book A First Course in Optimization written by Charles Byrne and published by CRC Press. This book was released on 2014-08-11 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Give Your Students the Proper Groundwork for Future Studies in OptimizationA First Course in Optimization is designed for a one-semester course in optimization taken by advanced undergraduate and beginning graduate students in the mathematical sciences and engineering. It teaches students the basics of continuous optimization and helps them better

Shapes and Geometries

Author : M. C. Delfour
Publisher : SIAM
ISBN 13 : 0898719364
Total Pages : 637 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Shapes and Geometries by : M. C. Delfour

Download or read book Shapes and Geometries written by M. C. Delfour and published by SIAM. This book was released on 2011-01-01 with total page 637 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the latest groundbreaking theoretical foundation to shape optimization in a form accessible to mathematicians, scientists and engineers.

Introduction to Derivative-Free Optimization

Author : Andrew R. Conn
Publisher : SIAM
ISBN 13 : 0898716683
Total Pages : 276 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Introduction to Derivative-Free Optimization by : Andrew R. Conn

Download or read book Introduction to Derivative-Free Optimization written by Andrew R. Conn and published by SIAM. This book was released on 2009-04-16 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first contemporary comprehensive treatment of optimization without derivatives. This text explains how sampling and model techniques are used in derivative-free methods and how they are designed to solve optimization problems. It is designed to be readily accessible to both researchers and those with a modest background in computational mathematics.

Introduction to Derivative-free Optimization

Author : Andrew R. Conn
Publisher : SIAM
ISBN 13 : 0898718767
Total Pages : 277 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Introduction to Derivative-free Optimization by : Andrew R. Conn

Download or read book Introduction to Derivative-free Optimization written by Andrew R. Conn and published by SIAM. This book was released on 2009-01-01 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: The absence of derivatives, often combined with the presence of noise or lack of smoothness, is a major challenge for optimisation. This book explains how sampling and model techniques are used in derivative-free methods and how these methods are designed to efficiently and rigorously solve optimisation problems.

Engineering Design Optimization

Author : Joaquim R. R. A. Martins
Publisher : Cambridge University Press
ISBN 13 : 110898861X
Total Pages : 653 pages
Book Rating : 4.1/5 (89 download)

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Book Synopsis Engineering Design Optimization by : Joaquim R. R. A. Martins

Download or read book Engineering Design Optimization written by Joaquim R. R. A. Martins and published by Cambridge University Press. This book was released on 2021-11-18 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on course-tested material, this rigorous yet accessible graduate textbook covers both fundamental and advanced optimization theory and algorithms. It covers a wide range of numerical methods and topics, including both gradient-based and gradient-free algorithms, multidisciplinary design optimization, and uncertainty, with instruction on how to determine which algorithm should be used for a given application. It also provides an overview of models and how to prepare them for use with numerical optimization, including derivative computation. Over 400 high-quality visualizations and numerous examples facilitate understanding of the theory, and practical tips address common issues encountered in practical engineering design optimization and how to address them. Numerous end-of-chapter homework problems, progressing in difficulty, help put knowledge into practice. Accompanied online by a solutions manual for instructors and source code for problems, this is ideal for a one- or two-semester graduate course on optimization in aerospace, civil, mechanical, electrical, and chemical engineering departments.