John Canny, in his paper "A Computational Approach to Edge Detection" (PDF), finds the expression of an optimal edge detector by first using an analytical approach (Euler-Lagrange equation). The coefficients of the solution still undetermined, a numerical optimization method is used to determine these coefficients. But the paper only provides a table of example values without any mention of the method used to calculate the coefficients.
I am trying to find optimal detectors for several profiles based on Canny's approach in this paper, but now I find myself unable to make any progress because of the lack of information on the method used.
Do you have an idea about the numerical optimization method used to calculate the coefficients? Any resources to read, details or just a simple description of this method would be very helpful.