  In this paper, we consider the unconstrained multiobjective optimization
problem. In recent years, researchers pointed out that the steepest decent
method may generate small stepsize which leads to slow convergence rates. To
address the issue, we propose a global Barzilai and Borwein's gradient
normalization descent method for multiobjective optimization (GBBN). In our
method, we propose a new normalization technique to generate new descent
direction. We demonstrate that line search can achieve better stepsize along
the descent direction. Furthermore, we prove the global convergence of
accumulation points generated by GBBN as Pareto critical points and establish a
linear rate of convergence under reasonable assumptions. Finally, we evaluated
the effectiveness of the proposed GBBN method based on the quality of the
approximated Pareto frontier and computational complexity.
