Nonmonotone Globalization Techniques for the Barzilai-Borwein Gradient Method

In this paper we propose new globalization strategies for the Barzilai and Borwein gradient method, based on suitable relaxations of the monotonicity requirements. In particular, we define a class of algorithms that combine nonmonotone watchdog techniques with nonmonotone linesearch rules and we prove the global convergence of these schemes. Then we perform an extensive computational study, which shows the effectiveness of the proposed approach in the solution of large dimensional unconstrained optimization problems.