The calculation of partial derivatives is a fundamental need in scientific computing. Automatic differentiation (AD) can be applied straightforwardly to obtain all necessary partial derivatives (usually first and, possibly, second derivatives) regardless of a codes complexity. However, the space and time efficiency of AD can be dramatically improved - sometimes transforming a problem from intractable to highly feasible - if inherent problem structure is used to apply AD in a judicious manner.
This book discusses the efficient use of AD to solve real problems, especially multidimensional zero-finding and optimization, in the MATLAB environment. This book is concerned with the determination of the first and second derivatives in the context of solving scientific computing problems with an emphasis on optimization and solutions to nonlinear systems. The authors focus on the application rather than the implementation of AD, solve real nonlinear problems with high performance by exploiting the problem structure in the application of AD, and provide many easy to understand applications, examples, and MATLAB templates.
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Discusses efficient use of automatic differentiation to solve real problems, especially multidimensional zero-finding and optimization in the MATLAB environment.
Chapter 1: Fundamentals of Automatic Differentiation and the Use of
ADMAT
Chapter 2: Products and Sparse Problems
Chapter 3: Using ADMAT with the MATLAB Optimization Toolbox
Chapter 4: Newtons Method and Optimization
Chapter 5: Structure
Chapter 6: Combining C/Fortran with ADMAT
Chapter 7: AD for Inverse Problems with an Application to Computational
Finance
Chapter 8: A Template for Structured Problems
Chapter 9: R&D Directions
Appendix A: Installation of ADMAT
Appendix B: How Are Codes Differentiated?
Thomas F. Coleman is a Professor in the Department of Combinatorics and Optimization, as well as the Ophelia Lazaridis University Research Chair, at the University of Waterloo. He is also the Director of WatRISQ, an institute composed of finance researchers that spans several faculties at the university. From 2005 to 2010, Dr Coleman was Dean of the Faculty of Mathematics at the University of Waterloo. Prior to this, he was Professor of Computer Science at Cornell University. He was also Director of the Cornell Theory Center (CTC), a supercomputer applications center, and founded and directed CTC-Manhattan, a computational finance venture. Dr Coleman has authored three books on computational mathematics, edited six conference proceedings, and published over 80 journal articles in the areas of optimization, automatic differentiation, parallel computing, computational finance, and optimization applications. Wei Xu is Research Manager at the Global Risk Institute (GRI), Toronto. Before joining GRI, Dr Xu was a Visiting Professor at the University of Waterloo. Previously, he was an Associate Professor at Tongji University, Shanghai. He co-founded Shanghai Raiyun Information Technology Ltd, a risk management services and solutions provider, and currently serves as its Director of R&D. His research has been featured in over 30 publications and he has co-authored a book on risk management.
