Numerical Experiments with Matrices Storage Free BFGS Method for Large Scale Unconstrained Optimization

We study the numerical performance of a matrices storage free quasi-Newton method for large-scale optimization, which we call the F-BFGS method. We compare its performance with that of the limited memory BFGS, L-BFGS methods developed by Nocedal (1980) and the conjugate gradient methods. The F-BFGS method is very competitive due to its low storage requirement and computational labor and also able to solve large-scale problems with 106 variables successfully while other methods fail.