Procedures to check the adjoint equations when using the method of steepest ascent

The method of steepest ascent is well documented in the literature [1]. However, its application to problems of high order (over 20) is not straightforward [2]. One problem that arises in the application of the method of steepest ascent, particularly to problems of high order and generally to problems of any order, is the pinpointing of errors in programming or in deriving the adjoint equations. This correspondence presents a systematic method for pinpointing such errors. First, a derivation of equations pertinent to the method of steepest ascent as developed by Bryson et al. [1] is presented. Then checks on the adjoints are followed by an illustrative example of the use of these checks.