An assessment of non-monotone linesearch techniques for unconstrained optimization

The purpose of this paper is to discuss the potential of nonmonotone techniques for enforcing convergence of unconstrained minimization algorithms from starting points distant from the solution. Linesearch-based algorithms are considered for both small and large problems, and extensive numerical experiments show that this potential is sometimes considerable. A new variant is introduced in order to limit some of the identified drawbacks of the existing techniques. This variant is again numerically tested and appears to be competitive. Finally, the impact of preconditioning on the considered methods is examined.