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Author: Simon Serovajsky
Publisher: CRC Press
ISBN: 1498750958
Category : Mathematics
Languages : en
Pages : 539
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Book Description
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.
Author: Simon Serovajsky
Publisher: CRC Press
ISBN: 1498750958
Category : Mathematics
Languages : en
Pages : 539
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Book Description
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.
Author: George Corliss
Publisher: Springer Science & Business Media
ISBN: 1461300754
Category : Computers
Languages : en
Pages : 431
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Book Description
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.
Author: Andrew R. Conn
Publisher: SIAM
ISBN: 0898716683
Category : Mathematics
Languages : en
Pages : 276
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Book Description
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.
Author: Donald R. Smith
Publisher: Courier Corporation
ISBN: 9780486404554
Category : Mathematics
Languages : en
Pages : 406
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Book Description
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.
Author: Andreas Griewank
Publisher: SIAM
ISBN: 0898716594
Category : Mathematics
Languages : en
Pages : 448
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Book Description
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.
Author: Regina S. Burachik
Publisher: Springer Science & Business Media
ISBN: 1441904379
Category : Mathematics
Languages : en
Pages : 237
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Book Description
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.
Author: Lorenz T. Biegler
Publisher: Springer Science & Business Media
ISBN: 364255508X
Category : Mathematics
Languages : en
Pages : 347
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Book Description
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.
Author: L. Cesari
Publisher: Springer Science & Business Media
ISBN: 1461381657
Category : Science
Languages : en
Pages : 555
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Book Description
This book has grown out of lectures and courses in calculus of variations and optimization taught for many years at the University of Michigan to graduate students at various stages of their careers, and always to a mixed audience of students in mathematics and engineering. It attempts to present a balanced view of the subject, giving some emphasis to its connections with the classical theory and to a number of those problems of economics and engineering which have motivated so many of the present developments, as well as presenting aspects of the current theory, particularly value theory and existence theorems. However, the presentation ofthe theory is connected to and accompanied by many concrete problems of optimization, classical and modern, some more technical and some less so, some discussed in detail and some only sketched or proposed as exercises. No single part of the subject (such as the existence theorems, or the more traditional approach based on necessary conditions and on sufficient conditions, or the more recent one based on value function theory) can give a sufficient representation of the whole subject. This holds particularly for the existence theorems, some of which have been conceived to apply to certain large classes of problems of optimization. For all these reasons it is essential to present many examples (Chapters 3 and 6) before the existence theorems (Chapters 9 and 11-16), and to investigate these examples by means of the usual necessary conditions, sufficient conditions, and value function theory.
Author: Morton I. Kamien
Publisher: Courier Corporation
ISBN: 0486310280
Category : Mathematics
Languages : en
Pages : 402
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Book Description
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.
Author: Boris S. Mordukhovich
Publisher: Springer Science & Business Media
ISBN: 3540312471
Category : Mathematics
Languages : en
Pages : 598
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Book Description
Comprehensive and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces Presents numerous applications to problems in the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc.
