Nonmonotone Proximal Gradient Method for Composite Multiobjective Optimization Problems

Abstract In this paper, we introduce proximal gradient methods with non-monotone Armijo line search rule of both kinds, max-type and average-type, to solve composite multiobjective optimization problems (CMOP). Moreover, the convergence analysis is given, and we show that all accumulation points of a sequence generated by both of the two kinds of nonmonotone proximal gradient methods are Pareto stationary points of (CMOP). Finally, we present numerical experiments illustrating the practical performance of these methods