The Broyden–Fletcher–Goldfarb–Shanno algorithm is a type of mathematical algorithm used to try and find the best solution to a certain problem. It works by starting at an initial starting point and then making small changes (called updates) to it, to try and find the best solution for the problem. As the algorithm runs, it records each update made and compares it to the previous update to see if it's getting closer to the best solution or not. If it is, then the algorithm keeps making changes, and if it isn't, it stops and returns the best solution found so far.