Enriched Methods for Large-Scale Unconstrained Optimization

This paper describes a class of optimization methods that interlace iterations of the limited memory BFGS method L BFGS and a Hessian free Newton method HFN in such a way that the information collected by one type of iteration improves the performance of the other Curvature information about the objective function is stored in the form of a limited memory matrix and plays the dual role of preconditioning the inner conjugate gradient iteration in the HFN method and of providing a warm start for L BFGS iterations The lengths of the L BFGS and HFN cycles are adjusted dynamically during the course of the optimization Numerical experiments indicate that the the new algorithms is very e ective and is not sensitive to the choice of parameters