Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.

Numerical Optimization

Survey of Numerical Methods for Trajectory Optimization

This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Followingare chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book

http://www.inf.ufes.br/~luciac/comcie/JFNK-Knoll.pdf

Jacobian-free Newton-Krylov methods: a survey of approaches and applications

Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems

The numerical methods employed in the solution of many scientific computing problems require the computation of derivatives of a function f $R^N$→$R^m$ Both the accuracy and the computational requirements of the derivative computation are usually of critical importance for the robustness and speed of the numerical solution Automatic Differentiation of FORtran (ADIFOR) is a source transformation tool that accepts Fortran 77 code for the computation of a function and writes portable Fortran 77 code for the computation of the derivatives In contrast to previous approaches, ADIFOR views automatic differentiation as a source transformation problem ADIFOR employs the data analysis capabilities of the ParaScope Parallel Programming Environment, which enable us to handle arbitrary Fortran 77 codes and to exploit the computational context in the computation of derivatives Experimental results show that ADIFOR can handle real-life codes and that ADIFOR-generated codes are competitive with divided-difference approximations of derivatives In addition, studies suggest that the source transformation approach to automatic differentiation may improve the time to compute derivatives by orders of magnitude

/pdf/adifor-generating-derivative-codes-from-fortran-programs-3amthpbrbz.pdf

ADIFOR-Generating Derivative Codes from Fortran Programs

Numerical codes that calculate not only a result, but also the derivatives of the variables with respect to each other, facilitate sensitivity analysis, inverse problem solving, and optimization. The paper considers how Adifor 2.0, which won the 1995 Wilkinson Prize for Numerical Software, can automatically differentiate complicated Fortran code much faster than a programmer can do it by hand. The Adifor system has three main components: the AdiFor preprocessor, the ADIntrinsics exception-handling system, and the SparsLinC library.

Adifor 2.0: automatic differentiation of Fortran 77 programs

Automatic differentiation is a technique for computing the derivatives of functions described by computer programs. ADIFOR implements automatic differentiation by transforming a collection of FORTRAN 77 subroutines that compute a function {line_integral} into new FORTRAN 77 suborutines that compute the derivaties of the outputs of {line_integral} with respect to a specified set of inputs of {line_integral}. This guide describes step by step how to use version 2.0 of ADIFOR to generate derivative code. Familiarity with UNIX and FORTRAN 77 is assumed.

/pdf/adifor-2-0-user-s-guide-revision-b-1gaehpx2wr.pdf

ADIFOR 2.0 user`s guide (Revision B)

An algorithm for constructing a precise call multigraph for languages that permit procedure parameters, extending the method of B. Ryder (see ibid., vol.5, no.3, p.216-225 (1979)) for handling recursion, is presented. If it is assumed that there is a constant upper bound on the number of procedure parameters to any procedure in the program, then the algorithm is polynomial in the total number of procedures in the program. >

Constructing the procedure call multigraph

The computation of large sparse Jacobian matrices is required in many important large-scale scientific problems. Three approaches to computing such matrices are considered: hand-coding, difference approximations, and automatic differentiation using the ADIFOR (automatic differentiation in Fortran) tool. The authors compare the numerical reliability and computational efficiency of these approaches on applications from the MINPACK-2 test problem collection. The conclusion is that ADIFOR is the method of choice, leading to results that are as accurate as hand-coded derivatives, while at the same time outperforming difference approximations in both accuracy and speed.

Alan Carle

Papers

ADIFOR-Generating Derivative Codes from Fortran Programs

Adifor 2.0: automatic differentiation of Fortran 77 programs

ADIFOR 2.0 user`s guide (Revision B)

Constructing the procedure call multigraph

Computing large sparse Jacobian matrices using automatic differentiation