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
requir ements. 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 ap
proach in the solution of large dimensional unconstrained optimization
problems.