Convergence of a nonmonotone projected gradient method for nonconvex multiobjective optimization

Abstract

We consider a nonmonotone projected gradient method for nonconvex multiobjective optimization problem. Under some mild assumptions, we prove that each accumulation point of the sequence generated by the algorithm, if exists, is Pareto stationary. Furthermore, when the nonmonotone line search in the algorithm is replaced by the monotone one, i.e., the classical Armijo search rule, the full convergence of the generated sequence to a Pareto stationary point (respectively, a weak Pareto optimal point) is established when the multiobjective function is quasiconvex (respectively, pseudoconvex). Numerical experiments are also presented to illustrate the effectiveness of this method.