Linear convergence of a nonmonotone projected gradient method for multiobjective optimization

摘要

We consider a projected gradient method equipped with the nonmonotone line search procedure for convex constrained multiobjective optimization problems. Under mild assumptions, we show the convergence of the full sequence generated by the algorithm to a weak Pareto optimal point. Furthermore, under some appropriate Lipschitz continuity assumption of the gradients of objective functions, a linear convergence result for this method is also established.