AUTOMATIC DIFFERENTIATION OF LARGE SPARSE SYSTEMS

With the advent of computer languages such as ADA and PASCAL-SC that allow the definition of new data types and the overwriting of operators it has become feasible to implement new algebras on a computer relatively simply. In the field of optimization when the objective function to be minimised F(x), xε{lunate}RN, can easily involve hundreds of arithmetic operations m, the task of deriving its gradient ∇F and Hessian ∇2F can be daunting and involve many man-days of effort. The classical alternative of estimating the value of the derivatives by difference formulae can lead to numerical limitation on the performance of the code and be computationally expensive. In this paper we discuss five new algebras that make both tasks redundant as with each the computer can accurately evaluate ∇F and ∇2F in far less time than the numerical difference formulae would imply. The interface between these algebras and the Truncated Newton Algorithm for unconstrained optimisation is also described. © 1990.