Spectral projected subgradient method with a 1-memory momentum term for constrained multiobjective optimization problem

In this paper, we propose a spectral projected subgradient method with a 1-memory momentum term for solving constrained convex multiobjective optimization problem. This method combines the subgradient-type algorithm for multiobjective optimization problems with the idea of the spectral projected algorithm to accelerate the convergence process. Additionally, a 1-memory momentum term is added to the subgradient direction in the early iterations. The 1-memory momentum term incorporates, in the present iteration, some of the influence of the past iterations, and this can help to improve the search direction. Under suitable assumptions, we show that the sequence generated by the method converges to a weakly Pareto efficient solution and derive the sublinear convergence rates for the proposed method. Finally, computational experiments are given to demonstrate the effectiveness of the proposed method.