LINEAR CONVERGENCE ANALYSIS FOR A NONMONOTONE PROJECTED GRADIENT ALGORITHM SOLVING MULTIOBJECTIVE OPTIMIZATION PROBLEMS

We consider a nonmonotone projected gradient algorithm for solving convex constrained multiobjective optimization problems. This scheme was proposed recently in [N. S. Fazzio and M. L. Schuverdt, Optim. Lett., 13 (2019), pp. 1365-1379], where the strong convergence of the sequence generated by the algorithm to a weak Pareto optimal solution was established. In this work, under some approximate assumptions of the gradients of objective functions, we obtain better convergence property, i.e., the linear convergence result for the algorithm. We also give some numerical implementations of this method and compare with other recent method in the literature.