Shortcuts
Shortcuts are a special-purpose technique to speed up initial convergence of the projections algorithm. An as-yet unpublished paper by Marco Krumbuegel and Rick Trebino describe the mathematics of this technique. Shortcuts appear to speed the algorithm by allowing the retrieval to jump out of local minima and approach the global minimum more closely. At errors of less than 1e-7, however, Shortcuts appear to hinder the convergence, rather than aid it. This is not usually a concern, since 1) no experimental data has ever come close to this level of convergence, and 2) at such low levels of error, the algorithm is already in the global minimum and normal projections or other algorithms work just as quickly.
Here is a graph showing the FROG error versus iteration for a theoretical, transform-limited pulse, using Projections with Shortcuts, and Projections without Shortcuts. See how the retrieval using Shortcuts initially converges faster, but stalls at about 1e-7.
