This paper proposes a novel variant of the proximal gradient method for a constrained multiobjective composite optimization problem, in which each objective function is the sum of a smooth function and a non-differentiable one. At each iteration, the descent direction of the differentiable part is calculated by solving a quadratic subproblem, and the non-differentiable part draws on the idea of the multi-objective proximal point method. Under locally Lipschitz continuity assumption, it is proved that the accumulation points of the sequence generated by the algorithm are Pareto critical. Under convexity condition, it is further proved that the sequence generated by the algorithm converges to a weak Pareto efficient point. We also establish the global convergence rates of the proposed approach. More specifically, we present the global convergence rates of O(1k) for convex case and O(rk) with some r∈(0,1) for strongly convex case, respectively. In addition, an application to a binary classification problem in supervised machine learning is given to validate the efficiency of the proposed method. Finally, performance experiments suggest that the proposed algorithm can robustly generate Pareto fronts of multiple synthesis test problems compared with existing ones.
Xu et al. (Tue,) studied this question.