Using ADIFOR 1.0 to Compute Hessians

1 1 Introduction 1 2 Procedure 1 3 Discussion 2 4 Initialization 3 5 Example 4 6 Conclusions 8 Appendix: ADIFOR-generated Subroutine for Computing Hessians 9 References 12 iii Using ADIFOR 1.0 to Compute Hessians by Paul Hovland Abstract ADIFOR provides a simple means to produce code for the first derivatives of functions through the technique of automatic differentiation. However, the fact that ADIFOR currently cannot produce code to compute second derivatives limits its usefulness for certain applications. This paper describes how ADIFOR and related tools can be used to produce code that does compute second derivatives and discusses how to use this code. Conclusions are presented about the limitations of this method and how it might compare with second-derivative code produced directly by ADIFOR. 1 Introduction When a scientist wishes to compute the gradient of a function for optimization or sensitivity analysis, ADIFOR provides a simple means to produce derivative code via auto..