Automatic differentiation in MATLAB using ADMAT with applications (Q2813268)

Automatic, or algorithmic differentiation (AD) is concerned with the efficient evaluation of partial derivatives of real-valued multivariate functions. For a comprehensive introduction to AD see [\textit{A. Griewank} and \textit{A. Walther}, Evaluating derivatives. Principles and techniques of algorithmic differentiation. 2nd ed. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (2008; Zbl 1159.65026)].NEWLINENEWLINEIn the textbook under review, the authors discuss the efficient use of AD to solve real problems, especially multidimensional zero-finding and optimization, in the MATLAB environment. This booklet is concerned with the determination of partial derivatives of first and second order in the context of solving scientific computing problems. All examples are illustrated with the use of the differentiator ADMAT which is available from \url{http://www.siam.org/books/se27}. This booklet is mainly written for engineers and applied scientists working in optimization, computational finance, or inverse problems.NEWLINENEWLINEThis textbook is divided into 9 chapters. The introductory Chapter 1 presents the gradient computation using ADMAT. Chapter 2 is devoted to the efficient computation of Jacobian/Hessian matrix-vector products. Chapter 3 illustrates how to use ADMAT with the MATLAB optimization toolbox. Chapter 4 demonstrates the efficient application of ADMAT for structured problems. Chapter 5 deals with Newton's method and optimization. Combining C/Fortran with ADMAT is described in Chapter 6. Chapter 7 deals with the use of AD for inverse problems arising in financial modeling. In Chapter 8, the authors introduce a collection of templates for structured problems. Some directions of researches and developments are sketched in Chapter 9. This booklet closes with 2 appendices, where one discusses the installation of ADMAT.