Optimization And Differentiation
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Author | : Simon Serovajsky |
Publisher | : CRC Press |
Total Pages | : 539 |
Release | : 2017-09-13 |
Genre | : Mathematics |
ISBN | : 1498750958 |
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 |
Total Pages | : 431 |
Release | : 2013-11-21 |
Genre | : Computers |
ISBN | : 1461300754 |
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 |
Total Pages | : 276 |
Release | : 2009-04-16 |
Genre | : Mathematics |
ISBN | : 0898716683 |
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 |
Total Pages | : 406 |
Release | : 1998-01-01 |
Genre | : Mathematics |
ISBN | : 9780486404554 |
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 |
Total Pages | : 448 |
Release | : 2008-11-06 |
Genre | : Mathematics |
ISBN | : 0898716594 |
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 |
Total Pages | : 237 |
Release | : 2010-11-25 |
Genre | : Mathematics |
ISBN | : 1441904379 |
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 |
Total Pages | : 347 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 364255508X |
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 |
Total Pages | : 555 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 1461381657 |
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 | : Boris S. Mordukhovich |
Publisher | : Springer Science & Business Media |
Total Pages | : 598 |
Release | : 2006-08-08 |
Genre | : Mathematics |
ISBN | : 3540312471 |
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.
Author | : Suvrit Sra |
Publisher | : MIT Press |
Total Pages | : 509 |
Release | : 2012 |
Genre | : Computers |
ISBN | : 026201646X |
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.