Reversal Strategies for Adjoint Algorithms

Adjoint Algorithms are a powerful way to obtain the gradients that are needed in Scientific Computing. Automatic Differentiation can build Adjoint Algorithms automatically by source transformation of the direct algorithm. The specific structure of Adjoint Algorithms strongly relies on reversal of the sequence of computations made by the direct algorithm. This reversal problem is at the same time difficult and interesting. This paper makes a survey of the reversal strategies formalizations used to justify these strategies. 1 Why build Adjoint Algorithms? Gradients are a powerful tool for mathematical optimization. The Newton method for example uses the gradient to find a zero of a function, itera-tively, with an excellent accuracy that grows quadratically with the number of iterations. In the context of optimization, the optimum is a zero of th