A global Barzilai and Borwein's gradient normalization descent method for multiobjective optimization

Abstract: 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.