A Barzilai-Borwein descent method for multiobjective optimization problems

The steepest descent method proposed by Fliege and Svaiter has motivated the research on methods for multiobjective optimization, which received increasing attention in recent years. However, empirical results show that Armijo line search often a very small stepsize along direction, decelerates convergence seriously. This paper points out issue is mainly due to imbalances among objective functions. To address this issue, we propose Barzilai-Borwein optimization (BBDMO), dynamically tunes gradient magnitudes using Barzilai-Borwein’s rule direction-finding subproblem. We emphasize BBDMO produces sequence of new directions compared Morovati et al. With monotone nonmonotone techniques, prove accumulation generated are Pareto critical points, respectively. Furthermore, theoretical indicate can achieve better BBDMO. Finally, comparative numerical experiments reported illustrate efficiency verify results.