next up previous [pdf]

Next: A comparison on a Up: Two solvers Previous: The fast L-BFGS method

A fair warning

Comparing the convergence of optimization techniques can be quite difficult to do in a fair manner. My steepest descent algorithm includes a termination criterion based on the Armijo rule only, namely, a sufficient decrease condition of the objective function (whereas L-BFGS use the Wolfe conditions). In addition, both the steepest descent and L-BFGS algorithms have different line-searches, which will affect convergence and computational performances. The L-BFGS line-search is based on the More and Thuente method, which uses bracketing and quadratic/cubic interpolation. The steepest-descent algorithm uses a very simple scheme where the step length is divided by two until the sufficient decrease condition is respected. Therefore, some of the computational differences come from the line-search algorithm and stopping criteria in addition to the inherent convergence properties of the two methods.